A straight magnetic strip has a magnetic moment of $44 \mathrm{Am}^{2}$. If the strip is bent in a semicircular shape, its magnetic moment will be \_\_\_\_ $\mathrm{Am}^{2}$. (Given $\pi=\frac{22}{7}$ )

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Magnetic Properties of Matter

A straight magnetic strip has a magnetic moment of

44 Am^{2}

. If the strip is bent in a semicircular shape, its magnetic moment will be ____

Am^{2}

.
(Given

π = \frac{22}{7}

)

Answer: 28

Solution

Straight strip: magnetic moment

M = m ℓ = 44

^{2}

, where

m

is pole strength and

ℓ

the length.

Bent into a semicircle of radius

r

: arc length

ℓ = π r ⟹ r = \frac{ℓ}{π}

. The effective moment now uses the straight-line distance between the poles, which is the diameter

2 r

M^{'} = m (2 r) = m \cdot \frac{2 ℓ}{π} = \frac{2 ( m ℓ )}{π} = \frac{2 \times 44}{π} = \frac{88 \times 7}{22} = 28 Am^{2}

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Integer answer

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