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A charge is distributed with a linear de...

A charge is distributed with a linear density `lamda` over a rod of the length L placed along radius vector drawn from the point where a point charge q is located. The distance between q and the nearest point on linear charge is R. The electrical force experienced by the linear charge due to q is

A

`(qlamdaL)/(4piepsilon_(0)R^(2))`

B

`(qlamdaL)/(4piepsilon_(0)R(R+L))`

C

`(qlamdaL)/(4piepsilon_(0)RL)`

D

`(qlamdaL)/(4piepsilon_(0)L^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
As coulomb's force is an action reaction pair, so force experenced by the linear charge is equal and opposite to the force experienced by point charge q. Here, we are computing electric force experienced by q due to the charge.
Considered a small element on line charge as shown, then force experienced by q due to this element is, `dF(qlamdadr)/(4piepsi_(0)r^(2))`
`F=intdF=overset(R+L)underset(R)int(qlamdadr)/(4piepsi_(0)r^(2))=(qlamdaL)/(4piepsi_(0)R(R+L))`
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