Question

1.
A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having
charge-Q. The radius of the sphere is 'a' and that of the spherical shell is 'b' (b> a). What is the electric field at
a distance R (a <R < b) from the centre ?
​

Answer 1

Answer:

3Q/(4πëR^2)

Explanation:

The electric field inside a shell/metallic sphere is always zero. We only need to consider the outside of the metallic sphere.

Answer 2

Concept:

To get the total electric field we will add the electric fields from both metallic sphere and the shell and the electric field inside any shell or any metallic sphere is zero, so we only need to consider the Electric field though metallic sphere.

Given:

Charge on solid metallic sphere = 3Q

Charge on spherical shell = - Q

The radius of the solid metallic sphere = 'a'

The radius of the spherical shell = 'b'

a < b

Find:

Electric field at a distance R ( a < R < b )

Solution:

Electric field at R due to Spherical shell will be zero.

So we only need to consider the Electric field though metallic sphere.

According to formula,

Electric field at r due to metallic sphere ( R > a ) = (KQ)/r²

Where, K = 1 / ( 4 π ε₀ )

In our case the charge on metallic sphere is + 3Q

So, Electric field at R due to metallic sphere ( a < R < b ) = (3KQ)/R²

Hence, Electric field at R due to metallic sphere ( a < R < b ) will be (3KQ) / R² where, K is 1 / ( 4 π ε₀ ) .

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