Chapter 24, Problem 98A

a.

To determine

The direction of the electric field between the plates.

Explanation of Solution

Introduction:

When a potential difference is applied between two conducting plates, it generates electric field directed from a higher to a lower potential or from positive to negative.

In an electric field, an electron moves towards the higher potential or to the positive side. The direction of the electric field is from the positive to the negative plate.

Hence, the direction of the electric field is from $P_2$ to $P_1$

Conclusion:

Electric field is from $P_2$ to $P_1$

b.

To determine

The speed of the electron at plate $P_2$ .

Answer to Problem 98A

  $v=8.4\times {10}^7\text{ m/s}$

Explanation of Solution

Given:

Charge on an electron, $q=1.6\times {10}^{-19}\text{ C}$

Potential difference, $\Delta V=2\times {10}^4\text{}\text{ V}$

Mass of an electron, $m=9.11\times {10}^{-31}\text{ kg}$

Formula Used:

  $K=\frac{1}{2}m{v}^2$

  $K=q\Delta V$

q is the charge

K is the kinetic energy

m is the mass of the charged particle

v is the velocity of the charged particle.

Calculations:

The total energy supplied to the electron is

  $\begin{array}{c}K=q\Delta V\\ =\left(1.6\times {10}^{-19}\text{ C}\right)\left(2\times {10}^4\text{}\text{ V}\right)\\ =3.2\times {10}^{-15}\text{J}\end{array}$

This energy supplied by the electric field applies a force on the electron which starts moving.

The velocity of the electron is calculated by

  $\begin{array}{l}K=\frac{1}{2}m{v}^2\\ v=\sqrt{\frac{2K}{m}}\end{array}$

  $v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2\left(3.2\times {10}^{-15}\text{ J}\right)}{9.11\times {10}^{-31}\text{ kg}}}$

  $v=8.4\times {10}^7\text{ m/s}$

Conclusion:

The speed of the electron at plate, $P_2$

  $v=8.4\times {10}^7\text{ m/s}$

c.

To determine

The motion of the electron in the magnetic field.

Explanation of Solution

Introduction:

A charged particle moving in a magnetic fieldexperiences force, the direction of which could be determined by Fleming’s left-hand rule.

Using the rule, the electron will move in a clockwise direction in the magnetic field.

Conclusion:

The electron will move in a clockwise direction in the magnetic field.