Chapter 21.1, Problem 11PP

To determine

Net charge on the sphere.

Answer to Problem 11PP

  $q=-3.125\times {10}^{-9}\text{C}$

Explanation of Solution

Given:

Electric field $E=2.625\times {10}^4\text{N/C}$ towards the sphere.

Distance from small sphere, $d=0.25\text{m}$ .

Formula Used:

Strength of electric field at distance d away from point charge is given by,

  $E=K\frac{q}{d^2}$

Where, $E$ is electric field strength, $K$ is Coulomb’s constant, $q$ is the point charge and $d$ is distance from the point charge.

Calculation:

Since, $K=9\times {10}^9{\text{Nm}}^2/{\text{C}}^{\text{2}}$

Assume small sphere as a point charge.

So, on putting the values,

  $\begin{array}{l}450=\left(9\times {19}^9\right)\times \frac{q}{{0.25}^2}\\ q=\frac{450\times {0.25}^2}{9\times {19}^9}\text{C}\\ =3.125\times {10}^{-9}\text{C}\end{array}$

As, electric filed is directed inward for negative point charge.

Since, the electric field lines are directed toward the sphere. It means charge on sphere is negative.

So, $q=-3.125\times {10}^{-9}\text{C}$

Conclusion:

Therefore, the net charge on sphere is $q=-3.125\times {10}^{-9}\text{C}$ .