Question

at the center of the neutral metal block, what is the direction of the electric field contributed by the charge in and on the metal block only?

Answer 1

The direction of electric field by the charge in and on the metal block will be along the direction line 5 as given in question.

How to determine electric field direction in a metal block?

The charge always remain on outer surface of metal and inside the metal block, the net electric field is zero. But due to dipole there is an electric field at the center of metal block i.e. at point R along direction line 1.

Now, to make make the net electric field zero at center, the electric field by the charge in and on the metal block must be equal in magnitude to that of electric field due to dipole at point R and in opposite direction to that of the net electric field at at R due to dipole.

The electric field by the charge in and on the metal block will be making 180° angle to the  electric field due to dipole at point R.

Hence the direction of electric field by the charge in and on the metal block will be along the direction line 5 as given in question.

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