Note that as \(\rho\) increases from zero to \(a\) (i.e., inside the wire), the magnetic field is proportional to \(\rho\) and therefore increases. It is known that B=(mu)H, but what mu should it be, i.e: mu of air or mu of the magnet since we measure B on air closer to the magnet and not inside the magnet? a steady (DC) current will be distributed uniformly throughout the wire (Section 6.4). Near the north pole, therefore, all H -field lines point away from the north pole (whether inside the magnet or out) while near the south pole all H -field lines point toward the south pole (whether inside the magnet or out). The magnetic field is most commonly defined in terms of the Lorentz force it exerts on moving electric charges. Answer of Ethylene glycol has a chemical formula of C2H6O2, a molar mass of 62.07 g mol and a density of 1.11 g cm3 . Since we determined above that \({\bf H}\cdot\hat{\bf z}\) is also zero, \({\bf H}\) must be entirely \(\pm\hat{\bf \phi}\)-directed. The total magnetic field, B = B 1 + B 2 The magnitude of the magnetic field produced by a current carrying straight wire is given by, r = 2 m, I = 10A. = The "integral form" of the original Ampre's circuital law[1] is a line integral of the magnetic field around any closed curve C (This closed curve is arbitrary but it must be closed, meaning that it has no endpoints). The magnetic field strength of magnet can be measured by Gauss Meter, or Tesla Meter. where are the references for those equations? a t Magnetic field strength is defined as the . magnetic force, attraction or repulsion that arises between electrically charged particles because of their motion. Since the current is uniformly distributed over the cross section, \(I_{encl}\) is less than the total current \(I\) by the same factor that the area enclosed by \({\mathcal C}\) is less than \(\pi a^2\), the cross-sectional area of the wire. . I . We show below how to obtain the formula for the magnetic . 2. Reassociating the known direction, we obtain: \[{\bf H} = \hat{\bf \phi}\frac{I_{encl}}{2\pi \rho} \nonumber \]. The magnetic flux density can be found using the following equation: B=0(H+M). , . The voltage is reduced as a result of the line integral of E field between any two points. , has current &=2 \pi \rho H(\rho) a Aus welchen Quellen wurden diese Gleichungen entnommen? { "7.01:_Comparison_of_Electrostatics_and_Magnetostatics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.02:_Gauss\u2019_Law_for_Magnetic_Fields_-_Integral_Form" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.03:_Gauss\u2019_Law_for_Magnetism_-_Differential_Form" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.04:_Ampere\u2019s_Circuital_Law_(Magnetostatics)_-_Integral_Form" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.05:_Magnetic_Field_of_an_Infinitely-Long_Straight_Current-Bearing_Wire" : "property get [Map 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The magnetic field is \(+\hat{\bf \phi}\)-directed for current flowing in the \(+z\) direction, so the magnetic field lines form concentric circles perpendicular to and centered on the wire. ), The distance from the source current, It is the basic force responsible for such effects as the action of electric motors and the attraction of magnets for iron. Solution is less than 1. around it. , then the magnetic field at the at a distance If this were not the case, then the field would not be radially symmetric. around a loop {\displaystyle n'} Please refer to the appropriate style manual or other sources if you have any questions. Omissions? 50. Magnetic Field Units. The magnetic force between two moving charges may be described as the effect exerted upon either charge by a magnetic field created by the other. {\displaystyle {\hat {n}}} The operator need to avoid the deviation from instrument and operation process. Next, the direction of each magnetic field's contribution is determined by drawing a circle centered at the point of the wire and out toward the desired point. Welcome to use our surface gauss calculators! there is a difference. 2 By definition, magnetic intensity Solution. If desired, the associated magnetic flux density can be obtained using \({\bf B} = \mu {\bf H}\). This equation is derived from one of Maxwell's equations called Ampere's law . What is the magnetic field strength at point 2 in the figure? 50. 2. electric field at equatorial,axial and at any point 3.gauss law , E.F at centre of loop 4. ampere circuital law and it's application 5.magnetic field at centre of loop,axial,equitorial,and at any point 5. capacitance of parallel plate capacitor,energy stored in capacitor and inductor Therefore, the right-hand rule specifies that positive \(I_{encl}\) corresponds to current flowing in the \(+z\) direction, which is consistent with the direction indicated in Figure \(\PageIndex{1}\). direction and as a magnitude of: (This represents the magnetic field at https://www.kjmagnetics.com/calculator.asp Since the currents are flowing in opposite directions, the net magnetic field is the difference between the two fields generated by the coils. It is known as the magnetomotive force (mmf) in analogy to the electromotive force (emf) which establishes current in an electric circuit. The magnetic field strength at the center of a circular loop is given by B = 0I 2R (at center of loop), B = 0 I 2 R (at center of loop), where R is the radius of the loop. where z is the distance from the center of the loop. Example: Find the magnitude and direction of magnetic field at the center of the semicircle given below. s I_{e n c l} &=\int_{\phi=0}^{2 \pi}[\hat{\phi} H(\rho)] \cdot(\hat{\phi} \rho d \phi) \\ It should be noted that the measured value of Nickel-coated magnets magnetic field strength will lower than Biot-Savart simulation value due to shielding effect from ferromagnetism Nickel coating. ), Ampere's law becomes: The equation says that the integral of the magnetic field The relative measurement of magnetic properties includes magnetic field strength, magnetic flux and magnetic moment. B I 7 Sponsored by Ultimate Dog Food Guide Make sure your dog is not eating any of this food. Plugging in the values into the equation, For the second wire, r = 4 m, I = 5A Plugging in the values into the equation, B = B 1 + B 2 (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. More accurate ones are complicated and depend on the shape of the loop, not just its area. The direction of B is given by the right-hand rule. Example: Directions of i and i currents are opposite. The problem is illustrated in Figure \(\PageIndex{1}\). I It is defined as the force experienced by a unit positive charge placed at a particular point. The finite element analysis technology is widely used in the design of sensor magnet, magnet assembly, and complex magnet system. Finally, we point out another "right-hand rule" that emerges from this solution, shown in Figure 7.5. Finally, we point out another right-hand rule that emerges from this solution, shown in Figure \(\PageIndex{2}\) and summarized below: The magnetic field due to current in an infinite straight wire points in the direction of the curled fingers of the right hand when the thumb of the right hand is aligned in the direction of current flow. is the number of turns per unit length. z This simple rule turns out to be handy in quickly determining the relationship between the directions of the magnetic field and current flow in many other problems, and so is well worth committing to memory. through any surface spanning the loop, plus a term depending on the rate of change of the electric field It can achieve the same as or even higher accuracy than Gauss-FFT through fewer sampling points. [2][3] {\displaystyle N} Ampere's law is given by the following equation: where is the magnetic field, is an infinitesimal line segment of the current carrying wire, is the permeability of free space, . d Solution Since the wire is a cylinder, the problem is easiest to work in cylindrical coordinates with the wire aligned along the \(z\) axis. Too, a north pole feels a force in the direction of the H -field while the force on the south pole is opposite to the H -field. L {\displaystyle \mathbf {B} \,} If /ell is the length of that path, then the total current enclosed is n'/ell, Basic Magnetic Terms definition with Formulas, - click to see images of magnetic field lines -, Physics equations/Magnetic field calculations, Magnetic field lines for typical geometries, Maxwell's correction term (displacement current), Magnetic field due to a long straight wire, Magnetic field inside a long thin solenoid. The 'displacement current' term provides a second source for the magnetic field besides current; the rate of change of the electric field is a unit vector pointing along the axis. points downward because the element at the top of the loop was chosen. Let us know if you have suggestions to improve this article (requires login). For simple shape magnet, we can calculate its approximate magnetic field strength by Biot-Savart law. {\displaystyle I\,} The magnetic field is going to be equal to 1.3 times 10 to the minus seventh teslas. The constant m 0 is the magnetic permiability. A magnetic field is produced by moving electric charges and intrinsic magnetic moments of elementary particles associated with a fundamental quantum property known as spin. {\displaystyle Id{\vec {\ell }}} This page titled 7.5: Magnetic Field of an Infinitely-Long Straight Current-Bearing Wire is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Steven W. Ellingson (Virginia Tech Libraries' Open Education Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. A magnetic field is a vector field in the neighbourhood of a magnet, electric current, or changing electric field in which magnetic forces are observable. The magnetic field $\overrightarrow{\boldsymbol{B}}$ at all points within the colored circle shown in Fig. where ^ For multi-polar magnet, the magnetic field strength will be measured by Magnet Analyzer. {\displaystyle {\hat {z}}} The calculated values and simulation results are for reference only, and the deviation between measured value and calculated value from various reasons. where is a unit vector that points in the azimuthal direction, and N E If an EM wave is directly . Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. E All right reserved. In this case, the relative measurement of magnetic properties is the best solution. The magnetic vector potential A is a vector field, defined along with the electric potential (a scalar field) by the equations: [3] where B is the magnetic field and E is the electric field. A magnetic field's dimensional formula can be described as the representation of magnetic field units in terms of fundamental physical quantities with sufficient power. Find the magnetic field in z=0 plane at x=2.0m, y=4.0m. The angle is the angle between the current vector and the magnetic field vector. The field of a magnet is the sum of fields from all magnetized volume elements, which consist of small magnetic dipoles on an atomic level. 55. Our editors will review what youve submitted and determine whether to revise the article. Intensity of Magnetic field. Solution: We have, n = 500, L = 5, I = 10 ) Calculating the magnetic fields is a bit more difficult you can reffer to Lienard Wiechert Potential Share Cite Between the capacitor's plates, the electric field is increasing, so the rate of change of electric field through the surface {\displaystyle Id{\vec {\ell }}} I While every effort has been made to follow citation style rules, there may be some discrepancies. Your thumb shows the direction of magnetic field and four fingers show direction of current. For magnet users, how to confirm the grade and magnetic properties are still a long standing issue. However, as \(\rho\) continues to increase beyond \(a\) (i.e., outside the wire), the magnetic field is proportional to \(\rho^{-1}\) and therefore decreases. a . 29.31 has an initial magnitude of 0.750 10:02 You make a seesaw by placing a 50 -g magnet (whose poles' faces are 2-cm-by-2-cm squares) at one end of a 50-cm-long ruler and a small $50-\m Magnetic field magnitude = B = Derivation of the Formula B = refers to the magnetic field magnitude in Tesla (T) = refers to the permeability of free space () {\displaystyle I\,} The magnetic field dimensional formula is M 1 T -2 I -1. The strength of magnetic field at a region inside a magnetic field is known as the magnetic field intensity. The force is zero if the second charge is travelling in the direction of the magnetic field and is greatest if it travels at right angles to the magnetic field. The magnetic field due to each wire at the desired point is calculated. The best way to find the direction of magnetic field due to a current carrying conductor is by using Fleming's right hand thumb rule. The magnetic force on a moving charge is exerted in a direction at a right angle to the plane formed by the direction of its velocity and the direction of the surrounding magnetic field. This term, the second term on the right, is the displacement current. [] surface gauss, magnetic flux, magnetic moment, and pull force. . {\displaystyle a} The problem is identical after any amount of rotation in \(\phi\); therefore, the magnitude of \({\bf H}\) cannot depend on \(\phi\). Of the four paths,only l1 is non-zero. The curve C bounds both a surface S, and any current which pierces that surface is said to be enclosed by the surface. {\displaystyle \mathbf {B} \,} d The electric field lines point from positive charges to negative charges. d Smaller circle has magnetic field ; It is the basic force responsible for such effects as the action of electric motors and the attraction of magnets for iron. The magnetic field has maximum magnitude when the angle between v v and r r is 90 90 and zero when the angle is 0 0 . But anyway, hopefully that gives you a little bit-- and just so you know how it all fits together. {\displaystyle z} is equal to the current Find the value of the magnetic field inside a solenoid of 5 m and 500 turns per unit length if 10A of current is passing through it. {\displaystyle dB_{\text{z}}=dBsin(\theta )} Therefore . z The magnetic fields follow the principle of super-position. 20.6. The magnetic field points in the direction of the . There is no relativity in here but causality is only taken into account. To get the given magnetic field the voltage has to be U ( t) = 1 C Q ( t) = 1 C d Q d t d t = 1 C B ( r) A 0 r d t = k a 2 + t 2 A 0 + const. Tangential Component Of Magnetic Field. \[\oint_{\mathcal C}{ {\bf H} \cdot d{\bf l} } = I_{encl} \label{m0119_eACL} \], where \(I_{encl}\) is the current enclosed by the closed path \({\mathcal C}\). component, so we multiply by the cosine of the acute angle in the right triangle shown: That vector potentials have a direct significance to quantum particles moving in magnetic fields is known as the A-B (Aharonov-Bohm) effect. ^ , Ampere's law yields: where *Problem: Show that in the vicinity of a long, straight wire carrying current The magnetic field lines inside the toroid are concentric circles. i are in fact related to the magnetization field M. The H -field, therefore, is analogous to the electric field E, which starts at a positive electric charge and ends at a negative electric charge. Formula of the Magnetic Field in Solenoi d To apply Ampere's law, consider an imaginary amperian loop in the shape of a rectangle \ (abcd,\) as shown in the below figure. The direct summation of all those dipole fields would require three-dimensional integration just to obtain the field of one magnet, which may be intricate.. C S 1. - 25. The Magnetic Circuits field intensity H causes a flux density B to be set up at every point along the flux path which is given by. is the magnetic constant. We study scattering by two solenoidal magnetic fields (pointlike magnetic fields) in two dimensions and analyze the asymptotic behavior of the scattering amplitude in the semiclassical limit. {\displaystyle \mathbf {E} \,} . . is the current, {\displaystyle L}. {\displaystyle d{\vec {B}}} For applications with no time varying electric fields (unchanging charge density) it is zero and is ignored. z I The magnetic field is unique at every point in space. The simplest way to solve for \({\bf H}\) from Equation \ref{m0119_eACL1} is to use a symmetry argument, which proceeds as follows: From the above considerations, the most general form of the magnetic field intensity can be written \({\bf H} = \hat{\bf \phi}H(\rho)\). To find the magnetic field formula due to an infinitesimally small current-carrying wire at some point, we use the Biot-Savart law to calculate the magnetic field of a highly symmetric configuration carrying a steady current Ampere's Circuital Law. ACL works for any closed path, so to exploit the symmetry of the cylindrical coordinate system we choose a circular path of radius \(\rho\) in the \(z=0\) plane, centered at the origin. d The magnetic field in a solenoid formula is given by, B = oIN / L B = (1.2610 6 15 360) / 0.8 B = 8.505 103 N/Amps m The magnetic field generated by the solenoid is 8.505 10 4 N/Amps m. Example 2: A solenoid of diameter 40 cm has a magnetic field of 2.9 105 N/Amps m. If it has 300 turns, determine the current flowing through it. ( 1 , we have our result. I Making the elements very (infinitely) short, we proceed from summation to integration of the contributions to the magnetic field from inidividual parts of the conductor. carries a current If a charge q is moving with a velocity v in uniform Magnetic field B, then from Lorentz equation we get the Magnetic force on the charge is F = q ( V B ) . Related Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? 2 In this formula, 'M' stands for mass, 'T' stands for time, and 'I' stands for current. For multi-pole magnetization and complex conditions, the designer willlearn its strength and distribution of magnetic field by finite element analysis software (FEA or FEM), then accurately estimate the magnetization state and flux distribution of whole magnetic circuit system. A magnetic field is basically used to describe the distribution of magnetic force around a magnetic object. 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If the magnetic field at the center of the circles is zero find the ratio of i to i i/i? . Magnetic Field Of A Point Charge With . According to the formula [3], the tangential component of the magnetic field will be discontinous if the boundary current (K) is greater than or equal to (-1). Using the formula for magnetic field we have, B = o IN/L = 4 10 -7 (400/2) 5 = 4 10 -7 200 5 = 12.56 10 -4 T Problem 2. From this point of view, the magnetic force F on the second particle is proportional to its charge q2, the magnitude of its velocity v2, the magnitude of the magnetic field B1 produced by the first moving charge, and the sine of the angle theta, , between the path of the second particle and the direction of the magnetic field; that is, F = q2B1v2 sin . SDM Magnetics have plenty of experience in finite element analysis of magnet application. https://en.wikipedia.org/w/index.php?title=Amp%C3%A8re%27s_circuital_law&oldid=578507291, https://commons.wikimedia.org/w/index.php?title=File:Displacement_current_in_capacitor.svg&oldid=38260258, https://en.wikiversity.org/w/index.php?title=Physics_equations/Magnetic_field_calculations&oldid=2329280. We seek only the The magnetic field deep inside the coil is generally aligned with axis of the coil as shown in Figure 7.6. The magnetic field produced by a steady current flowing in a very long straight wire encircles the wire. Part D What is the magnetic field direction at point 2 in the figure? flowing through a wire, which creates a magnetic field If we apply right hand rule, directions of currents are; Thus, total magnetic field at point O becomes the difference of these magnetic fields. , to the field point (at the center) is always , and since their cross product always points along the axis of the loop, we have. The constant 0 is known as the permeability of free space and is exactly. The Magnetic Field on Axis of Ring formula is defined as the magnitude of magnetic field produced by a circular conductor carrying current of value 'i' and radius 'r' at a distance 'd' from the centre of ring on its axis is calculated using Magnetic Field = ([Permeability-vacuum] * Electric Current * Radius ^2)/(2*((Radius ^2)+(Perpendicular Distance ^2))^(3/2)). z H = 2 10 5 T. Therefore, Torque which is acting on the magnet will be, = m H. Copyright 2022 SDM Magnetics Co.,Ltd. The formula to calculate magnetic field strength inside a loop is given by: where, N = Number of coils r = Coil radius [meters] Magnetic Field Strength Inside a Loop Calculator Now, let us look at the formula to calculate magnetic field strength inside a solenoid, where, n = number of turns/m Magnetic Field Strength Inside a Solenoid Calculator z The corresponding classical mechanical system has a . The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. RHR-2 gives the direction of the field about the loop. Moreover, we can show the direction of current inside the circle with following pictures; The magnetic field strength of magnet can be measured by Gauss Meter, or Tesla Meter. Surface gauss is referring to the magnetic field strength which measured at a certain point of magnets surface by Gaussmeter, and it is the most used [], ( ) . https://www.kjmagnetics.com/calculator.repel.asp. The SI unit of magnetic field is Tesla, T T. Note that the coulomb (C) per second is ampere (A). {\displaystyle {\hat {z}}} . For multi-polar magnet, the magnetic field strength will be measured by Magnet Analyzer. The units of flux density are weber (Wb)/m 2 called tesla (T). A smaller magnetic field unit is the Gauss (1 Tesla = 10,000 Gauss). n Substituting this into Equation \ref{m0119_eACL1}, we obtain, \begin{aligned} The strength of magnetic field at a point can be given in terms of vector quantity called magnetic intensity (H). . The magnetic field is an abstract entity that describes the influence of magnetic forces in a region. Changing the direction of integration should not change the magnetic field associated with the current!). Explains how to calculate the magnitude and direction of a magnetic field that is created by a moving point charge. carries a current in the figure to the right; the magnetic field points in the d 1T = 1 N C m/s = 1 N A m 1 T = 1 N C m/s = 1 N A m Use 4 1 0 Tm/A for the value of . {\displaystyle I\,} The standard SI unit for magnetic field is the Tesla, which can be seen from the magnetic part of the Lorentz force law F magnetic = qvB to be composed of (Newton x second)/(Coulomb x meter). This is shown by the circle with a dot in its center. Along the two straight sections of the loop, r and dl are parallel or opposite, and thus dl r = 0. Legal. At a point P a radial distance r away from the wire it has magnitude. The diagram shows a capacitor being charged by current When viewed from the +z-axis, the current is flowing clockwise. The one-dimensional equation has fixed points given by Eq. is perpendicular to The magnetic vector potential gets modified to A ( r, t) = 0 4 J ( r , t r ) | r r | d 3 r where t r = t 1 c | r r | is the retarded time. d. The magnetic pole model predicts correctly the field H both inside and outside magnetic materials, in particular the fact that H is opposite to the magnetization field M inside a permanent magnet. = S z Magnetic field is an invisible space around a magnetic object. {\displaystyle a\;d{\vec {\ell }}} Fleming's right hand thumb rule states that if one holds a current carrying in his right hand such that the thumb finger points the direction of current . , where. The magnetic field at a distance r from a long current-carrying conductor I, according to the law, is given by the equation B=0I2r Where, 0 is a special constant defined as the permeability of free space in the equation. In order to find the magnetic field formula, one would need to first find the magnetic flux density. magnetic force, attraction or repulsion that arises between electrically charged particles because of their motion. Corrections? Many thanks for your comment, please check this link: https://www.lakeshore.com/Documents/Measuring%20Perm%20Magnets%20App%20Note.pdf. Circular wire produces magnetic field inside the circle and outside the circle. found above. In order to ensure the hall element free of crack, the instrument manufacturer usually make an epoxy resin coating upon the hall element. We asses the magnetic field inside the toroid using the formula for the magnetic field in a solenoid because a toroid is in fact a solenoid whose ends are bent together to form a hollow ring. And that's why you don't have metal objects being thrown around by the wires behind your television set. {\displaystyle z} r In this section, we use the magnetostatic form of Amperes Circuital Law (ACL) to determine the magnetic field due to a steady current \(I\) (units of A) in an infinitely-long straight wire. 0=4107Tm/A. B d Do the line integral shown. through the surface. They exist when the right-hand side in Eq. S The need for this extra term can be seen in the figure to the right. The magnetic field at point P has been determined in Equation 12.15. {\displaystyle a} Direction of the magnetic field at the center of the circle is found with right hand rule. The magnetic field is + ^ -directed for current flowing in the + z direction, so the magnetic field lines form concentric circles perpendicular to and centered on the wire. This coating alsoproduce an air gap, and this air gap is often overlooked during calculation and simulation. For applications with no time varying electric fields (unchanging charge density) it is zero and is ignored. A magnetic field line can never cross another field line. The radial symmetry of the problem also requires that \({\bf H}\cdot\hat{\bf \rho}\) be equal to zero. The AS-FT algorithm has good adaptability to continuous medium, weak magnetic catastrophe medium, and strong magnetic catastrophe medium. 3. 2. {\displaystyle {\hat {r}}} This term, the second term on the right, is the displacement current. But if you're closer to to the loop than, say, ten times its radius (or side length or other characteristic dimension) these formulae become increasingly inaccurate. A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents,: ch1 and magnetic materials. This equation gives the force on a straight current-carrying wire of length in a magnetic field of strength B. Answer: The magnitude of the magnetic field can be calculated using the formula: The magnitude of the magnetic field is 6.00 x 10 -6 T, which can also be written as (micro-Tesla). The effective magnetic field \(\vec{h}_{\text{eff}}\) is the sum of the external, demagnetizing and anisotropy fields (see [1, 5] for more details). S.I. B = 0 I/ (2r). In case of a homogeneous magnetization, the problem can be simplified at least in two different . B Magnetic field around a circular wire is calculated by the formula; B=2k.i/r a Therefore, \(H(\rho)=I_{encl}/2\pi \rho\). Since the normal to the area is parallel to the length, dAdL equals dV, which is the volume element. B and advance your work. B-field: A synonym for the magnetic field. It also generates a magnetic field that points out of the page on the right side of the wire. 105. {\displaystyle \partial {\vec {E}}/\partial t} The magnetic field produced by a steady current flowing in a very long straight wire encircles the wire. When a magnetic compass points north it is aligning itself with Earth's magnetic field and points to the Magnetic North Pole, not the Geographic North Pole, which is actually about 310 miles (500 . Key Terms. (Heres an excellent exercise to test your understanding. B Thus the line integral over current becomes a volume integral: *Problem: Show that if circular loop of radius Change the direction of the path of integration and confirm that you get the same result obtained at the end of this section. ***Problem:Show that if circular loop of radius I Since the distribution of current is uniform and infinite in the \(z\)-dimension, \({\bf H}\) cant depend on \(z\), and so \({\bf H}\cdot\hat{\bf z}\) must be zero everywhere. {\displaystyle {\hat {\theta }}} is positive, and its magnitude gives the correct value for the field field Note that is the length of wire that is in the magnetic field and for which 0, as shown in Figure 20.19. 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