Three point charges each of charge q are located at three di

Three point charges, each of charge +q, are located at three different corners of a square of side length L. (i) Find the magnitude and direction of the electric field at the centre of the square. (ii) Find the electric potential at the centre of the square. A point charge, of charge +q and mass m, is brought from far away and placed at the centre of the square. (iii) How much work is done moving this charge? (iv) If the charge placed at the centre of the square is released, what is the acceleration of the charge at the instant of release? (v) The released charge will eventually pass through the fourth comer of the square. What will its velocity be when it does so?

Solution

Here,

for the three charges located at the corners

i) as the electric field due to diagonally oposite charges will cancel out

electric field to a single charge will remain.

mangitude of electric field = k * q/(L/sqrt(2))^2

mangitude of electric field = 2 * k * q/L^2

the direction of electric field towards the empty corner.

ii)

Now , for the potential at the centre

potential at the centre = 3 * k * q/(L/sqrt(2))

potential at the centre 3 * sqrt(2)*k * q/L

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iii) work done in moving the charge = Potential * charge

work done in moving the charge = 3 * sqrt(2)*k * q/L * q

work done in moving the charge = 3 * sqrt(2)*k * q^2/L

iv)

let the initial acceleration is a

Using second law of motion

m * a = q * 2 * k * q/L^2

a = k * q^2/(L^2 * m)

the acceleration of the charge at the instant of release is k * q^2/(L^2 * m)