a) Calculate the electric potential at the center of the square described as follows: Four charges are placed at the corners of a 20 cm square. The particles are as follows: 10 `mu`C at (0,0); -5 `mu`C at (20,0); -15 `mu`C at (20, 20); and 20 `mu`C at (0, 20).
b) What is the electric potential energy of the above configuration in part a?
Electric potential due to a system of charges placed in air is given by
`V = V_1 + V_2 + V_3 + ... + V_n`
=` ``1/(4piepsi_0)sum_(i=1)^nq_i/r_i `
= `1/(4piepsi_0)(q_1/r_1 + q_2/r_2 + q_3/r_3 + ... +q_n/r_n)`
Here, four charges have been placed at the corners of a 20 cm square. The electric potential at the center of the square has to be calculated.
the distance of the charges from the centre of the square, r should be equal to 1/2 the length of the diagonal.
r=`1/2*20sqrt2` = `10sqrt2` cm =`10sqrt2*10^-2` m
Therefore, V = `1/(4pi*(8.854*10^-12)*10sqrt2*10^-2)(10 + (-5) + (-15) + 20)*10^-6` Volts
= `10*10^-6/(4pi*(8.854*10^-12)*10sqrt2*10^-2)` Volts
= `6.355*10^5 ` Volts
Therefore, the electric potential at the centre of the square will be `6.355*10^5` Volts.