Eleven equal point charges , all of then having a charge `+Q` , are placed at all the hour positions of a circular clock of radius r, except at the 10 hour position . What is the electric field strength at the centre of the clock ?

Options

A. `(Q)/(4piepsilon_(0)r^(2))` from the centre towards the mark 10
B. `(Q)/(4piepsilon_(0)r^(2))` from the mark 10 towards the centre
C. `(Q)/(4piepsilon_(0)r^(2))` from the centre towards the mark 6
D. Zero

Answer

a

Explanation

Given ,radius of the circular clock = r and each of eleven position of a circular clock has a charge +Q.

`therefore` Electric field at the centre of the clock is
`E_(0)=E_(1)+E_(2)+E_(3)+E_(4)+E_(5)+E_(6)+E_(7)+E_(8)+E_(9)+E_(10)+E_(11)+E_(12)`
Now , `E_(1)andE_(7)` are opposite to each other , so they will cancel out each others effect.
Similarly `E_(2)andE_(8),E_(3)andE_(9),E_(5)andE_(11),E_(6)andE_(12)` will also cancel out their effect as they are opposite to each other.
`thereforeE_(c)=E_(4)=(1)/(4piepsilon_(0))(Q)/(r^(2))` (directed from the centre towards the maek 10)