Chapter 16, Problem 30P

To determine

The electric field strength at a point in space.

Answer to Problem 30P

The electric field strength at a point is $0.1\text{N/C}$ .

Explanation of Solution

Given:

Mass of proton, $m=1.67\times {10}^{-27}\text{kg}$

Acceleration,

  $\begin{array}{c}a=1\text{million}\times g\\ =g\times {10}^6\end{array}$

Formula used:

Write the expression to calculate the force using Newton’s second law.

  $F=ma$.... (1)

When the expression to calculate the electric force.

  $F=qE$ .... (2)

Where,

  $q$is the charge of proton.

  $E$ is the electric field strength.

Calculation:

Equate equation (1) and (2) to determine the electric field strength.

  $\begin{array}{c}qE=ma\\ E=\frac{ma}{q}\end{array}$

Substitute the values in the above expression.

  $\begin{array}{c}E=\frac{\left(1.67\times {10}^{-27}\text{kg}\right)\left({10}^6\times 9.8\right)}{\left(1.6\times {10}^{-19}\right)}\\ =0.1\text{N/C}\end{array}$

Conclusion:

Therefore, the electric field strength at a point is $0.1\text{N/C}$ .