Chapter 8, Problem 1RQ

To determine

Choose the correct option from the given choices to identify the statement that is not true about the electric force and magnetic force.

Answer to Problem 1RQ

The correct options from the given choices are (b) Both F_e and F_m depend on the velocity of the charged particle and (c) Both F_e and F_m can perform work.

Explanation of Solution

Calculation:

Write the general expression for electric force.

$F_e=QE$        (1)

Here,

$Q$ is the electric charge, and

$E$ is the electric field intensity.

Write the general expression for the magnetic force.

$F_m=Qu\times B$        (2)

Here,

u is the velocity,

$Q$ is the moving charge, and

$B$ is the magnetic flux density.

On observing Equation (2), the magnetic force $\left(F_m\right)$ depends on the velocity u, whereas in Equation (1), the electric force $\left(F_e\right)$ does not depend on the velocity u.

From Equation (2), it is clear that the magnetic force $F_m$ is perpendicular to both u and B. Here, $F_m$ cannot perform work since it is at right angles to the direction of motion of charge (that is, $F_m\cdot dl=0$) and also does not cause an increase in the kinetic energy of charge.

From the above explanation, it is clear that Options (b) and (c) are correct and Options (a), (d), (e), and (f) are incorrect.

Conclusion:

Thus, the correct options from the given choices are (b) Both F_e and F_m depend on the velocity of the charged particle and (c) Both F_e and F_m can perform work.