A single loop of wire of radius 3 cm carries a current of 29

A single loop of wire of radius 3 cm carries a current of 2.9 A. What is the magnitude of B on the axis of the loop at the following positions? (a) the center of the loop .0060736 T (b) 1 cm from the center .000051857 T (c) 2 cm from the center .0000399 T (d) 32 cm from the center .0000000493 T

Solution

Here,

r = 3 cm

I = 2.9 A

a) at the centre of loop

B = u0 * I/(2 r)

B = 4pi *10^-7 * 2.9/(2 * 0.03)

B = 6.07 *10^-5 T

b)
at x = 1 cm = 0.01 m

B = (u0/2) * r^2 * I/(x^2 + r^2 )^1.5

B = 4pi *10^-7/2 * 0.03^2 * 2.9/(0.01^2 + 0.03^2)^(1.5)

B = 5.18 *10^-5 T

c)

at x = 2 cm = 0.02 m

B = (u0/2) * r^2 * I/(x^2 + r^2 )^1.5

B = 4pi *10^-7/2 * 0.03^2 * 2.9/(0.02^2 + 0.03^2)^(1.5)

B = 3.49 *10^-5 T

d)

at x = 32 cm =0.32

B = (u0/2) * r^2 * I/(x^2 + r^2 )^1.5

B = 4pi *10^-7/2 * 0.03^2 * 2.9/(0.32^2 + 0.03^2)^(1.5)

B = 4.94 *10^-8 T