The Biot-Savart law

Problem:

(a)  A circular loop of wire of radius R carries a current I.  Find the magnetic induction B on the axis of the loop, as a function of the distance z from the center of the loop.
(b)  Use the result to find B at points on the axis of a solenoid of radius R and length L wound with n turns per unit length.
(c)  Use this result to find the self-inductance of a very long solenoid (L >> R).

Solution:

Problem:

A circuit in the form of a regular polygon of n sides is circumscribed about a circle of radius a.  
(a)  If it is carrying a current I, find the magnitude of the magnetic field B at the center of the circle in terms of μ0, n, I, and a.  
(b)  Find B at the center of the circle as n is indefinitely increased.  

Solution:

Similar problems

Problem:

Find the magnetic field at the center of a circular loop of radius R that is formed in a long straight thin wire that carries current I; use the SI system of units.

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Solution:

Problem:

In practical magnetic structures, uniform magnetic fields are frequently necessary.  The uniformity of the field produced by Helmholtz coils, or two co-axial loops which carry currents in the same direction, is one of their most important characteristics.  Assume that the coils have a radius a, have axes on the x-axis, carry current I each, and are separated by a distance b.

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(a)  Find the magnetic field at a point P on the axis of the loops and a distance x from the midpoint O.
(b)  Expand the expression for the field in a power series, retaining terms to order x2.
(c)  What relationship must exist between a and b such that the x2 terms vanish?  What is the significance of this?
(d)  Show that the field created by the coils to this order and under the conditions established in part c is given by Bx = 8I/(53/20c2).

Solution:

Problem:

An AC voltage source V(t) = V0sinωt is connected to a wire of resistance R which forms a circular loop of radius a.  The wire loop rotates about the z-axis with angular frequency ω.  Find the instantaneous and the average magnetic field B (magnitude and direction) at the center of the loop.  Neglect the self-inductance of the loop.

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Solution: