Suppose that there exists a U-shaped current-carrying wire with current I as sho

Question

Suppose that there exists a U-shaped current-carrying wire with current I as shown in Fig. 1. Find the magnetic field (magnitude and direction) at point (1). Assume that the straight parts of the wire extend infinitely far to the right, and that the circular part has a radius a. Remember that the magnitude of the magnetic field at a distance d from an infinite wire is:

(a) Find the magnetic field (magnitude and direction) at point (1).

(b) What would be the magnitude of the magnetic field at (1), if I = 2.0 A and a = 0.02 m?

Explanation / Answer

using right hand thumb rule, magnetic field due to the upper section,

the semi circle and the lower section will be out of the page.

magnetic field due to a semiinfinte straight wire is given by

B=mu*I/(4*pi*r)

as both upper section and lower section have same magnetic field and both are in thr same dirrection

net field due to both the straight wires=mu*I/(2*pi*r)

where r=distance of center of semi circle from each of the striaght line

=radius of the semicirlce

field due to the semicircle=mu*I/(2*r)

hence total field=(mu*I/(2*pi*r))+(mu*I/(2*r))

part b:

using I=2 A

mu=4*pi*10^(-7)

r=0.02 m

we get total magnetic field magnitude=8.2832*10^(-5) T

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