A circular loop of wire having a radius of 8.90 cm carries a current of 0.133 A.

Question

A circular loop of wire having a radius of 8.90 cm carries a current of 0.133 A. A vector of unit length and parallel to the dipole moment of the loop is given by 0.60i Overscript EndScripts – 0.80j Overscript EndScripts. If the loop is located in a uniform magnetic field given by Upper B Overscript right-arrow EndScripts = (0.770 T)i Overscript EndScripts + (0.111 T)k Overscript EndScripts, find (a) the x-component, (b) the y-component, and (c) the z-component of the torque on the loop and (d) the magnetic potential energy of the loop.

Explanation / Answer

here

i x j = k, j x k = i, k x i = j, a x b = - b x a, and a × a = 0

t = IAu' × B
= I * A [ (0.60i - 0.80j) × (0.77i + 0.111k)]
= I * A [ (0.462(i×i) + 0.0666(i × k) - 0.616(j × i) - 0.0888(j × k)]
= I * A (-0.0666j + 0.616k - 0.0888i)

then

I = 0.133 amp

A = pie * r^2 = 3.14 * 0.089^2 = 0.0248 m^2

then by putting the values

0.133 * 0.0248 *( -0.0888i - 0.0666j + 0.616k)

(-2.9 * 10^-4 i - 2.2 *10^-4 j + 2.03 *10^-3 k)

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