Question

A loop carrying current i in xy plane the unit vector k cap is coming out of plane of paper the magnetic moment of current loop is​

Answer 1

Answer:

[(π/2) + 1]a2 I k

Explanation:

Given Problem:

A loop carrying current i in xy plane the unit vector k cap is coming out of plane of paper the magnetic moment of current loop is​?

Solution:

To Find:

Magnetic moment of current loop.

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Method:

A1 = Area of central square = $(side)^2 = a^2$

A2 = area of all focus semicircles == 4 × (πr²/2) = 2πr²

Here radius = $\frac{a}{2}$

Hence,

A2 = 2π(a/2)² = 2π × (a²/4) = (πa²/2)

Total area = A1 + A2 = a² + (π/2)a² = a²[1 + (π/2)]

Magnetic moment = M = IA = Ia²[1 + (π/2)]k