Question

A charge Q is placed at the centr of the square of side 2.10 cm, at the corners of which four identical charges q = 7.5 C are placed. Find the value of the charge Q so that the whole system is in equilibrium.

Answer 1

Given is:-

Side of the square a=2.10 cm or   

Four identical charges with  

q = 7、5C

The diagonal distance is  

Now,

Let consider the charge on the top left corner, the forces experienced by this charge are as shown below:-

F d F C qLd

Now the value of the forces are

by plugging all the values we get

which gives us

15

The resultant of these two forces will be in the direction of F_c and will be

Fod 1.15 x105)(1.15 x 1015)2

or

Fed 1.63 1015Л

Now,

  

which gives us

now the total force experienced by the top left charge in the direction of F_c is

by plugging all the values we get

F,et = 8.12 × 1014 + 1.63 × 101

which gives us

Therefore the midpoint charge should be of negative polarity so that in can counter this net force, therefore

which gives us

This should be the required charge on to the midpoint charge so that the whole system remains in equilibrium