Chapter 20, Problem 4Q

To determine

In what direction is the force on the wire?

Answer to Problem 4Q

Solution:

The force on the wire is vertically downward.

Explanation of Solution

Introduction:

$\begin{array}{l}d\overrightarrow{f}=id\overrightarrow{l}\times \overrightarrow{B}\\ d\overrightarrow{f}:\text{force on small element}\\ d\overrightarrow{l}:\text{ is current element}\\ \overrightarrow{B}:\text{ magnetic field}\end{array}$

Magnetic field outside the magnet is form north to south.

Small force is given by $\text{d<mover accent="true"><mn>f</mn><mo>→</mo></mover> = id<mover accent="true"><mn>l</mn><mo>→</mo></mover>}\times \text{<mover accent="true"><mn>B</mn><mo>→</mo></mover>}$ it is cross product of current element and magnetic field.

Direction of magnetic field is given by right hand rule.

Move you four fingers of right hand toward the current in such way that you can curl your four fingers towards the $\overrightarrow{B}$, then vertically of thumb gives direction of force. That is vertically down ward.