Question

Chapter 28, Problem 055 Two concentric, circular wire loops of radii r -18.5 am and r2 30.0 cm, are located in an xy plane; each carries a clockwise current of 7.77 A (see the figure below). (a) Find the magnitude of the net magnetic dipole moment of the system, (b) Repeat for reversed current in the inner loop. (a) Number (b) Number

Answer 1

Magnetic moment is given by:

$\mu$ = I*A = I*pi*r^2

I = Current in loop

r = radius of loop

Part A. when current in both loop is in same direction (clockwise)

$\mu$_net = $\mu$_outer + $\mu$_inner

$\mu$_net = I*pi*(r_outer)^2 + I*pi*(r_inner)^2

$\mu$_net = I*pi*((r_outer)^2 + (r_inner)^2)

r_outer = 30 cm = 0.3 m

r_inner = 18.5 cm = 0.185 m

I = current in both loops = 7.77 A

So,

$\mu$_net = 7.77*pi*(0.3^2 + 0.185^2)

$\mu$_net = 3.03 A-m^2

From right hand law net magnetic moment will be into the page

Part B:

when current in both loop is in same direction (clockwise)

$\mu$_net = $\mu$_outer - $\mu$_inner

$\mu$_net = I*pi*(r_outer)^2 - I*pi*(r_inner)^2

$\mu$_net = I*pi*((r_outer)^2 - (r_inner)^2)

r_outer = 30 cm = 0.3 m

r_inner = 18.5 cm = 0.185 m

I = current in both loops = 7.77 A

So,

$\mu$_net = 7.77*pi*(0.3^2 - 0.185^2)

$\mu$_net = 1.36 A-m^2

From right hand law net magnetic moment will be into the page

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