A very large, charged plate floats in deep space. Due to the charge on the plate, a constant electric field E exists everry above the plate. An object with mass m and charge q is shot upward from the plate with a velocity v and at an angle `theta`. It follows the path shown reaching a height h and a ramge R. Assume the effects of gravity to be negligible.

Which of the following will result in an increase in R?

Options

A. Increasing both q and m by a factor of 2
B. Decreasing both q and m by factor of 2
C. Increasing q by a factor of 2 while decreasing m by a factor of 2
D. Decreasing q by a factor of 2 while increasing m by a factor of 2

Answer

D

Explanation

`a=(qE)mrArr m uarr rArr a darr rArr h=(u^(2) sin^(2) theta)/(2xx(qE)/m)`
`rArr h prop m/q [tan u, theta & E "is constant"]`