Chapter 6, Problem 51SGA

To determine

The angle of the wire to the magnetic field.

Explanation of Solution

Given information:

The force of the current is $0.2Newton.$

The current in the wire is $5\text{ amperes}\text{.}$

Length of the wire is $1\text{ meters}.$

Magnetic induction is $0.04\text{ Newtons per amper meter}\text{.}$

Calculation:

The magnetic induction is given by the formula,

  $\begin{array}{l}B=\frac{F}{IL\sin \theta },\\ Where,\\ B\to \text{ Magnetic induction}\text{.}\\ F\to \text{ Force on a current}\text{.}\\ I\to \text{ Current}\text{.}\\ L\to \text{ Length of the wire}\text{.}\\ \sin \theta \to \text{angle of the wire to the magnetic field}\text{.}\end{array}$

Now putting all the values in the equation, we get

  $\begin{array}{l}B=\frac{F}{IL\sin \theta },\\ 0.04=\frac{0.2}{5\times 1\times \sin \theta },\\ 0.04\times 5\times 1\times \sin \theta =0.2\\ 0.2\sin \theta =0.2\\ \sin \theta =1\\ \theta ={\sin }^{-1}1\\ \theta =90°\end{array}$

Thus the angle of the wire to the magnetic field is $90°$ .