When a hollow metal sphere is charged, the electric field inside the sphere is zero, and the charge resides only on the surface of the sphere. Therefore, the electric field intensity at a distance x from the centre of the sphere is given by:

E = kQ/x^2

Where, k is the Coulomb constant, Q is the charge on the sphere, and x is the distance from the centre of the sphere.



Given, the potential difference between the surface of the sphere and a point at a distance 3r from the centre is V. Hence, the electric field intensity at a distance 3r from the centre is given by:

V = E*3r

Or, E = V/3r

Also, for a hollow charged metal sphere, the charge resides only on the surface of the sphere. Therefore, the charge on the sphere is given by:

Q = 4πr^2σ

Where, σ is the surface charge density of the sphere.

Thus, the electric field intensity at a distance 3r from the centre of the hollow charged metal sphere is given by:

E = kQ/(3r)^2

Substituting the value of Q, we get:

E = k(4πr^2σ)/(3r)^2

Or, E = (4/9)kπrσ

Therefore, the electric field intensity at a distance 3r from the centre of the hollow charged metal sphere is (4/9) times the product of Coulomb's constant, π, radius of the sphere, and surface charge density of the sphere.

Hence, the electric field intensity at 3r distance from the centre of the hollow charged metal sphere is (4/9)kπrσ, where k is the Coulomb constant, r is the radius of the sphere, and σ is the surface charge density of the sphere.