Question

A non-conducting sphere of radius 1.0 m carrying net positive charge 18nC is
enclosed by a concentric non-conducting thin spherical shell of radius 2.0 m
carrying net negative charge 20 nC. Determine the electric fields at the distances
of 0.5 m, 1.5 m, and 2.5 m, respectively, from the centre of the sphere.​

Answer 1

Given: A non-conducting sphere of radius 1.0 m carrying net positive charge 18nC, thin spherical shell of radius 2.0 m  carrying net negative charge 20 nC.

To find: The electric fields at the distances  of 0.5 m, 1.5 m, and 2.5 m, respectively, from the centre of the sphere.

Solution:

• Now we have given the radius as 0.5 m, So according to Gauss law:

              ∫E dA = 1 / ∈o ∑q(i)

              E x 4πr² =  1 / ∈o x { q /( 4/3 x π x R1³) } x 4/3 x π x r³

              E = q1 x r / 4π∈oR1³ = 18 x 10^9 x 0.5 / 4 x 3.14 x 8.85 x 10^-12 x 1³

• After calculations, it comes out to be: 162 V/m

• Now r = 1.5, we have:

              ∫E dA = 1 / ∈o ∑q(i)

              E x 4πr² =  1 / ∈o x q1

              E = q1 / 4π∈o x r² = 18 x 10^9 / 4 x 3.14 x 8.85 x 10^-12 x (1.5)²

• After calculations, it comes out to be: 72 V/m

• Now r = 2.5, we have:

             ∫E dA = 1 / ∈o ∑q(i)

             E x 4πr² =  1 / ∈o x (q1 - q2)

             E = q1 - q2 / 4π∈o x r² = (18 - 20) x 10^9 / 4 x 3.14 x 8.85 x 10^-12 x (2.5)²

• After calculations, it comes out to be: -1.31 V/m

Answer:

                 So the electric fields at the distances  of 0.5 m, 1.5 m, and 2.5 m, respectively are 162 V/m , 72 V/m and -1.31 V/m from the centre of the sphere.