Chapter 25.1, Problem 1PP

(a)

To determine

To Calculate: The EMF which is induced in the wire.

Answer to Problem 1PP

EMF induced in the wire is $4\text{V}$ .

Explanation of Solution

Given:

For a straight wire,

  $l=0.5\text{m =}$ Length of the wire.

  $\nu \text{=20}\text{m/s=}$ Speed relative to the field.

  $\text{B=0}\text{.4}\text{T=}$ Motional EMF.

Formula used:

To calculate the EMF of a straight wire formula used is,

  $EMF=Blv\sin \left(\theta \right)$

Where,

  $B$ , Motional EMF

  $l$ , Length of wire given.

  $v$ , Speed relative to the field

Calculation:

In the first step by using the formula for EMF,

The formula is

  $EMF=Blv\sin \left(\theta \right)$

Substituting the given values in the above formula,

  $\begin{array}{l}EMF=Blv\sin \left(\theta \right)\\ =\left(0.4\text{T}\right)\times \left(0.5\text{m}\right)\times \left(20\text{m/s}\right)\times \left(1\right)\\ =4\text{V}\end{array}$

Conclusion:

Hence, EMF which is induced in the wire is $4\text{V}$ .

(b)

To determine

To calculate:

The current of the wire.

Answer to Problem 1PP

The current of a straight wire is $0.66\approx 0.7\text{A}$

Explanation of Solution

Given:

Electromotive force, EMF $=4\text{V}$

Resistance, $R=0.6\Omega$

Formula used:

  $I=\frac{EMF}{R}$

Where,

  $I=$ Current

  $R=$ Resistance

Calculation:

The formula for current used is,

  $I=\frac{EMF}{R}$

Substituting the values in above formula,

  $I=\frac{0.4\text{V}}{6.0\Omega }=0.66\text{A}$

Conclusion:

Hence, the current of a straight wire is $0.66\approx 0.7\text{A}$ .