A loop ABCD is moving with velocity v towards the right. The magnetic field is 2 T . Loop is connected to a resistance of 9 Ω . If the steady current of 2 A flows in the loop, then the value of v , if

Question

A loop ABCD is moving with velocity v towards the right. The magnetic field is 2 T . Loop is connected to a resistance of 9 Ω . If the steady current of 2 A flows in the loop, then the value of v , if loop has resistance of 4 Ω , is (Given AD = 30 cm )

TestHub · Accepted Answer

When a straight conductor moves with velocity v perpendicular to the magnetic field then emf induced is given by $V = B v l$ . Here, it will be $V = B v (l \sin θ)$ .

Potential difference is $V = B v (l \sin θ)$

$V = 2 \times v \times \frac{30}{100} \times \frac{1}{2} = 0 \cdot 3 v$

Now, $Current = \frac{V}{R}$

$\Rightarrow 2 = \frac{0 \cdot 3 V}{13}$

$\Rightarrow v = 86 .7 {m s}^{- 1}$

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