Chapter 28, Problem 63A

a.

To determine

To calculate: If the ratio $E/B$ has to be changed in selecting particles of the same velocity.

Answer to Problem 63A

  $E/B$ ratio will remain same for same values of velocity.

Explanation of Solution

Given:

The J.J. Thomson’s cathode ray tube is modified to accelerate protons rather than electrons.

Formula used:

Velocity is given by,

  $v=\frac{E}{B}$

Where $E$ is the strength of the electric field and $B$ is the strength of the magnetic field..

Calculation:

Since particles of the same velocity are to be selected, the $E/B$ ratio will remain same as $v=\frac{E}{B}$ .

Hence, it is obvious that if velocity will be the same, $E/B$ ratio will also be the same.

Conclusion:

  $E/B$ ratio will remain same for same values of velocity.

b.

To determine

To calculate: If $B$ is larger or smaller for a deflection caused by the magnetic field to remain the same.

Answer to Problem 63A

For the deflection to remain the same, magnetic field strength needs to be larger.

Explanation of Solution

Given:

The J.J. Thomson’s cathode ray tube is modified to accelerate protons rather than electrons.

Formula used:

Magnetic force is given by,

  $Bqv=\frac{m{v}^2}{r}$

Where $B$ is the strength of the magnetic field, $q$ is the charge, $v$ is velocity, $m$ is mass and $r$ is radius.

Calculation:

The deflection caused by the magnetic field is calculated as:

  $r=\frac{mv}{Bq}$

For a larger mass, $B$ must be larger for $r$ to be constant.

Conclusion:

For the deflection to remain the same, magnetic field strength needs to be larger.