A pair of long conducting rails are held vertical at a separation $l = 50 c m$ . The top ends are connected by a resistance of $R = 0.5 Ω$ and a fuse (F) of negligible resistance. A conducting rod is free to slide along the rails under gravity. The whole system is in a uniform horizontal magnetic field B = 1.5T as shown. Resistance of the rod and rails are negligible and the rod remains horizontal as it moves. The rod is released from rest. Find the maximum mass of the rod in $10^{- 3} k g$ that will ensure that the fuse does not blow out. It is known that rating of the fuse is 4A. Take $g = 10 m / s^{2}$ and neglect self-induction.

Question

A pair of long conducting rails are held vertical at a separation $l = 50 c m$ . The top ends are connected by a resistance of $R = 0.5 Ω$ and a fuse (F) of negligible resistance. A conducting rod is free to slide along the rails under gravity. The whole system is in a uniform horizontal magnetic field B = 1.5T as shown. Resistance of the rod and rails are negligible and the rod remains horizontal as it moves. The rod is released from rest. Find the maximum mass of the rod in $10^{- 3} k g$ that will ensure that the fuse does not blow out. It is known that rating of the fuse is 4A. Take $g = 10 m / s^{2}$ and neglect self-induction.

Accepted Answer

When current in the circuit is I = 4A, magnetic force on the rod is $F = I l B = 4 \times 0.5 \times 1.5 = 3 N$
The weight of the rod must exceed F to blow out the fuse
$∴ m g \geq 3 ∴ m \geq \frac{3}{10} = 0.3 k g$

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