Question

Electric field given by the vector $\overrightarrow{E}=x\hat{i}+y\hat{j}$ is present in the xy plane. A small ring carrying charge +Q, which can freely slide on a smooth nonconducting rod, is projected along the rod from the point (0, L) such that it can reach the other end of the rod. What minimum velocity should be given to the ring? (Assume zero gravity)

• A. $(Q{L}^2/m{)}^{1/2}$
• B. $2(Q{L}^2/m{)}^{1/2}$
• C. $4(Q{L}^2/m{)}^{1/2}$
• D. zero

Answer 1

The correct option is D zero

Applying energy conservation
$\Delta K+\Delta U=0$
or $(0-\frac{1}{2}m{v}^2)+q\Delta V=0$ (i)
$dV=-Edx-Edy$
${\int }_{V_1}^{V_2}dV=-[\int E_{x}dx+\int E_{y}dy]$
$\Delta V=-[{\int }_0^{L}xdx+{\int }_L^{0}ydy]=0$
Hence using equation (i), we get v = 0