Question

4 equal point charges each 16uC are placed on the 4 corners of a square of side 0.2m . calculate the force on any 1 of the charges?

Answer 1

Suppose,the `4` like charges are present at `A,B,C,D` and `AB=BC=CD=DA=0.2m`

We are considering forces on `B`;so due to `A` and `C` force(`F`) will be repulsive in nature along `AB` and `CB` respectively.

due to `D` force (`F'`) will also be repulsive in nature acting along diagonal `DB`

`DB=0.2sqrt(2)m`

So,`F=(9*10^9*(16*10^-6)^2)/(0.2)^2 =57.6N`

and `F'=(9*10^9*(16*10^-6)^2)/(0.2sqrt(2))^2=28.8N`

now,`F'` makes an angle of `45^@` with both `AB` and `CB`.

so,component of `F'` along two perpendicular direction i.e `AB` and `CB` will be `28.8 cos 45`

So,we have two forces of `(57.6+28.8 cos 45)=77.95N` acting perpendicular to each other on the charge at `B`

So,net force on the charge at `B` is `sqrt(77.95^2 +77.95^2)=77.95 sqrt(2)=110.24N` making an angle of `45^@` w.r.t `AB` and `CB`