Chapter 27, Problem 27.1DQ

Can a charged particle move through a magnetic field without experiencing any force? If so, how? It not, why not?

To determine

Whether a charged particle moves through the magnetic field without experiencing the force.

Answer to Problem 27.1DQ

Yes, the charged particle can move through magnetic field without experiencing any magnetic force.

Explanation of Solution

A charged particle experiences magnetic force when the velocity and magnetic field are at right angle. The charged particle experiences zero magnetic force when the particle moves along the direction of magnetic field i.e., the velocity and the magnetic field are at parallel or antiparallel direction to each other.

Formula to calculate force is,

$F=qvB\sin \left(\varphi \right)$

If the charged particle moves in the direction of magnetic field, then the angle $\left(\varphi \right)$ becomes $0°$.

Substitute $0°$ for $\varphi$.

$\begin{array}{c}F=qvB\sin \left(0°\right)\\ =0\end{array}$

Therefore, the force becomes zero if magnetic field and the velocity are in parallel direction or in antiparallel direction to each other.

Conclusion: Yes, the charged particle can move through magnetic field without experiencing any magnetic force.