A current carrying loop of radius $2 c m$ has $4 A$ current flowing in an anti-clockwise direction. The plane of the loop makes an angle of $θ$ with the direction of the magnetic field which is in an upward direction. the value of the magnetic field is $0.7 T e s l a$ .if potential energy of loop in magnetic field is $\approx 0.01 J$ , then value of $θ$ is:

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Answer 1

Potential energy $= μ B = μ B cos θ$ where $μ =$ magnetic moment
$μ = i A$ where $A$ = Area of loop
$p_{E} = i A cos θ \times B = 0.01$
$0.7 \times 4 \times π \times 4 \times 10^{- 4} cos θ = 0.01$
$cos θ = \frac{0 . 0 1 \times 1 0 ^{- 4}}{1 6 π \times 0 . 7} = \frac{1 0 0}{5 0 \times 0 . 7} = \frac{2}{0 . 7}$
$cos θ > 1$ is not possible.
So option C is correct.

Answer 2

Potential energy

= μ B = μ B cos θ

where

μ =

magnetic moment

μ = i A

where

A

= Area of loop

p_{E} = i A cos θ \times B = 0.01

0.7 \times 4 \times π \times 4 \times 10^{- 4} cos θ = 0.01

cos θ = \frac{0 . 0 1 \times 1 0 ^{- 4}}{1 6 π \times 0 . 7} = \frac{1 0 0}{5 0 \times 0 . 7} = \frac{2}{0 . 7}

cos θ > 1

is not possible.

So option C is correct.