Question

A hollow sphere of radius a carries a total charge q distributed uniformly over its surface a small area of the sphere is cut off find the electric field at the centre due to the remaining sphere

Answer 1

Now let us assume the small amount of a negative charge is equal to  Q*dA/(4*pi*a^2) on a dA

SO it will make it neutral to cut the area of the meaning charge with positive and will disappear on it.

Therefore the negative charge will be pleased to be confused and the mass in the contribution on an electric field.

F=qE

1/(4*pi*e)*q^2/r^2 = qE

E=1/(4*pi*e)*q^2/r^2

putting in values

E=1/(4*pi*e)*[Q*dA/(4*pi*a^2)]^2/a^2

Answer 2

Small part 'AB' of hollow sphere of area 'dA' is cut off. Now, electric field at centre 'O' of system will only be due to part CD of area 'dA' directly in front of it. [rest is cancelled out]

Let charge on CD ⇒ dQ

So, dQ = Q / ( 4πa²) . dA

Electric field at O  = Eo = k(dQ) / a² = 1 / (4πℰo) * Q/4πa² dA. 1/a²

Eo = QdA / (16π²ℰoa⁴)