A particle of mass 2 × 10 - 5 kg moves horizontally between the plates of a parallel plate capacitor which produce an electric field of 200 N C - 1 in the vertically upward direction. A magnetic induc

Question

A particle of mass 2 × 10 - 5 kg moves horizontally between the plates of a parallel plate capacitor which produce an electric field of 200 N C - 1 in the vertically upward direction. A magnetic induction of 2.0 T is applied at right angles to the electric field in a direction normal to both E → and v → . If g is 9.8 m s - 2 and the charge on the particle is 10 - 6 C , then the velocity of the charged particle so that it continues to move horizontally is

TestHub · Accepted Answer

Net force on the particle should be zero.

$qE = 1 0^{- 6} \times 200 = 2 \times 1 0^{- 4} N$

$mg = 2 \times 1 0^{- 5} \times 9.8 = 1.96 \times 1 0^{- 4} N$

Since $qE > mg$ , so magnetic force $qvB$ should act downwards to balance the forces.

$qE = mg + qvB \Rightarrow 2 \times 1 0^{- 4} = 1.96 \times 1 0^{- 4} + 1 0^{- 6} v \times 2$

$\Rightarrow v = 2 m/s$

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