Question

A straight wire in a magnetic field experiences a force of 0.022 N when the current in the wire is 1.1 A. The current in the wire is changed, and the wire experiences a force of 0.067 N as a result. What is the new current?

Answer 1

The magnetic force that acts on the wire in the first case can be written as follows:

$$F_1=BI_1Lsin\theta.$$

The magnetic force that acts on the wire in the second case can be written as follows:

$$F_2=BI_2Lsin\theta.$$

Let's divide the first equation by the second one:

$$\dfrac{F_1}{F_2}=\dfrac{I_1}{I_2},$$ $$I_2=\dfrac{F_2I_1}{F_1}=\dfrac{0.067\ N\cdot1.1\ A}{0.022\ N}=3.35\ A.$$