6 Electrostatic shielding Consider a conductor with a cavity with no charges inside the cavity remarkable result is that the electric field inside the cavity is zero whatever be the size and shape of the cavity and whatever be the charge on the conductor and the external fields in which it might be placed We have proved a simple case of this result already the electric field inside a charged spherical shell is zero The proof of the result for the shell makes use of the spherical symmetry of the shell see Chapter 1 But the vanishing of electric field in the charge free cavity of a conductor is as mentioned above a very general result A related result is that even if the conductor Example 4 Strategy Mo p p 380 380 Net field E E E 1 In a uniform sphere of charge charge density p a small cavity is created The centre of cavity is at a distance a from the centre of sphere Taking centre of sphere as origin and as a unit vector along the line joining the centre of cavity and origin show that the electric field at any point inside the cavity is 300 Consider any point Pinside cavity The position vector of P is F The field at P can be assumed to be a superposition of field due to a uniform sphere of charge E and field due to a negative charged sphere of the size of cavity E P F 380 where position vector of Pw r t C pa pa 380 380 C a a you all Fields Since the field at point P does not depend on the position of point P in the ca