A small block of mass m and charge +q is kept on a smooth horizontal xy-plane. Both electric field and magnetic field are acting in the region given by E→=E0i^NC−1 and B→=B0j^ respectively at t=0. Block starts moving on the plane with zero velocity, then [Gravity acts along negative Z-direction]

N+Fm=mg N=O⇒Fm=mg qVB0=mg V=mgqB0 V=(qE0m)t t=m2gq2ε0B0

A small block of mass m and charge +q is kept on a smooth horizontal xy-plane. Both electric field and magnetic field are acting in the region given by E→=E0i^NC−1 and B→=B0j^ respectively at t=0. Block starts moving on the plane with zero velocity, then [Gravity acts along negative Z-direction]

N+Fm=mg N=O⇒Fm=mg qVB0=mg V=mgqB0 V=(qE0m)t t=m2gq2ε0B0

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A small block of mass m and charge $+ q$ is kept on a smooth horizontal xy-plane. Both electric field and magnetic field are acting in the region given by $\vec{E} = E_{0} \hat{i} N C^{- 1}$ and $\vec{B} = B_{0} \hat{j}$ respectively at $t = 0$ . Block starts moving on the plane with zero velocity, then [Gravity acts along negative Z-direction]

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After some time block moves with constant velocity

Block remains at rest at any instant

Block leaves the contact at an instant $t = \frac{m^{2} g}{q^{2} E_{0} B_{0}}$

Block leaves the contact when speed of the block is $\frac{m q}{q B_{0}}$

answer is B, D.

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Detailed Solution

$N + F_{m} = m g N = O \Rightarrow F_{m} = m g q V B_{0} = m g V = \frac{m g}{q B_{0}} V = (\frac{q E_{0}}{m}) t t = \frac{m^{2} g}{q^{2} ε_{0} B_{0}}$

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