Chapter 27, Problem 2P

To determine

(a) To determine:

The velocity of a beam of electrons.

Answer to Problem 2P

Solution:

The velocity of the beam of electrons is $7.2\times {10}^6\text{m/s}$.

Explanation of Solution

Given:

Electric field, $E=1.88\times {10}^4\text{V/m}$

Magnetic field, $B=2.60\times {10}^{-3}\text{T}$

Formula used:

The velocity of the electron beam is calculated by the formula

$v=\frac{E}{B}$

Here,

$E$ is the electric field

$B$ is the magnetic field

Calculation:

The velocity of the electron beam is calculated as

$v=\frac{E}{B}$

Plugging the values in the above equation

$\begin{array}{c}v=\frac{1.88\times {10}^4}{2.60\times {10}^{-3}}\\ =7.2\times {10}^6\text{m/s}\end{array}$

To determine

(b) To determine:

The radius of the electron orbit, if electric field is switched off.

Answer to Problem 2P

Solution:

The radius of the electron orbit is $\text{0}\text{.13}\text{mm}$.

Explanation of Solution

Given:

Electric field, $E=1.88\times {10}^4\text{V/m}$

Magnetic field, $B=2.60\times {10}^{-3}\text{T}$

Formula used:

In the absence of electric field the radius of the electron orbit is calculated as

$\frac{e}{m}=\frac{v}{Br}$

Here,

$B$ is the magnetic field

$e=1.6\times {10}^{-19}\text{C}$ is the charge of electron

$m=9.1\times {10}^{-31}\text{kg}$ is the mass of the electron

$v$ is the velocity of the electron

$r$ is the radius of the electron orbit

Calculation:

In the absence of electric field the radius of the electron orbit is calculated as

$\frac{e}{m}=\frac{v}{Br}$

Plugging the values in the above equation

$\begin{array}{c}\frac{1.6\times {10}^{-19}}{9.1\times {10}^{-31}}=\frac{6.2\times {10}^4}{2.60\times {10}^{-3}\times r}\\ r=0.00013\text{m}\\ =\text{0}\text{.13}\text{mm}\end{array}$