Answer to Question #157207 in Physics for Priya

Question

A non conducting solid sphere of radius 2.0m carrying net positive charge 20nC. Enclosed by a concentric non conducting thin spherical shell of radius 4.0m carrying net negative charge 25nC. Determine the electric fields at the distance of 1.0m,3.0m,and 10.0m respectively from the centre of the sphere

Answer 1

The field from the first solid non-conducting sphere of radius $a_1=2\text{ m}$ at a distance $r<a_1$:

$$E_1=\frac{kq_1r}{a_1^3}.$$

At $r>a_1$:

$$E_1=\frac{kq_1}{r^2}$$

The field from the second (radius $a_2=4\text{ m}$) thin insulating sphere inside it is 0, at $r>a_2$:

$$E_2=\frac{kq_2}{r^2}$$

Find the resultant field at different distances.

1) At $r=1\text{ m} \space(r<a_1<a_2)$:

$$E=E_1+E_2=E_1+0=E_1,\\\space\\ E=E_1=\frac{kq_1r}{a^3}=6.66\text{ V/m}.$$

2) At $r=3 \text{ m}\space(a_1<r<a_2)$:

$$E=E_1+E_2=E_1+0=E_1,\\\space\\ E=E_{1[r>a_1]}=\frac{kq_1}{r^2}=20\text{ V/m}.$$

3) At $r=10 \text{ m}\space(a_1<a_2<r)$:

$$E=E_1+E_2,\\\space\\ E=\frac{k}{r^2}(q_1-q_2)=-0.45\text{ V/m}.$$