In gravity free space, a bead of charge 1 μ C and mass 3 mg is threaded on a rough rod of friction coefficient μ = 0.3 . A magnetic field of magnitude 0.2 T exists perpendicular to the rod. The bead i

Question

In gravity free space, a bead of charge 1 μ C and mass 3 mg is threaded on a rough rod of friction coefficient μ = 0.3 . A magnetic field of magnitude 0.2 T exists perpendicular to the rod. The bead is projected along the rod with a speed of 4m/s. How much distance (in m) will the bead cover before coming to rest?

TestHub · Accepted Answer

The magnetic force is perpendicular to velocity, so speed changes only due to friction; normal reaction N = qvB (gravity-free).

Retardation: $- μ q v B = m \frac{d v}{d t} = m v \frac{d v}{d S}$

$μ qB S = m v$

$S = \frac{m v}{μ qB} = \frac{3 \times 1 0 ^{- 6} \times 4}{0.3 \times 1 0 ^{- 6} \times 0.2} = 200 m$

Answer: 200.00

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