Electric field given by the vector `vec E = x hat i + y hat j` is present in the x y plane. A small ring carrying `+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).
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Options

A. `(Q L^2//m)^(1//2)`
B. `2(Q L^2//m)^(1//2)`
C. `4(Q L^2//m)^(1//2)`
D. `(Q L^2//2m)^(1//2)`

Answer

d

Explanation

`Delta K + Delta U = 0`
or `(0 + (1)/(2) mv^2) + q Delta V = 0`
`underset(V_(2))overset(V_(1))(int) d V = - [ int E_x d x + int E_y d y]`
`Delta V = - [underset(0)overset(L)int x d x + underset(L)overset(0)(int) y dy] = 0`
Hence `v = 0`.