Chapter 25, Problem 43A

To determine

To Calculate: Length of the wire and the angle between the field and velocity.

Answer to Problem 43A

The length of the wire is $23\text{m}$ and the angle is found to be $90°.$

Explanation of Solution

Given:

The force or the EMF produces the velocity of $4.0m/s$ in the given magnetic field of $0.050T$

  $\begin{array}{l}EMF=\text{4}\text{.5}\text{V}\\ v=4.0\text{m/s}\\ B=0.050\text{T}\end{array}$

Formula Used:

  $L=\frac{EMF}{Bv(sin\theta )}$

where,

  $B$ = Magnetic field

  $v=$ Velocity

  $L$ = Length

Calculation:

Length of the wire can be calculated by the formula,

  $L=\frac{EMF}{Bv(sin\theta )}$

Substituting the values in the above formula,

  $\begin{array}{l}=\frac{\text{4}\text{.5V}}{\text{(0}\text{.050}\text{T)(4}\text{.0}\text{m/s)(1)}}\\ =23\text{m}\end{array}$

The shortest length of the wire that can be used is of $23\text{m}$ and assuming that the wire and direction of motion are perpendicular to each other the angle is $90°$ .

Conclusion:

Hence, length of the wire is $2\text{3}\text{m}$ and the angle between the field and velocity $90°$ .