Chapter 25, Problem 64A

To determine

To Show:The units of $Blv$ are in volts.

Answer to Problem 64A

The unit substitution shows that the units of $Blv$ are in volts.

Explanation of Solution

Introduction:

The potential difference across the terminals of the battery is theelectromotive force or EMF. The EMF is measured in volts. When you move a wire through a field placed in magnetic field,a force is exerted on the charges and they start moving in the direction of the force. The work is done on the charges.

The Electromotive force is given by the formula,

  $EMF=Blv\left(\sin \theta \right)$

Where,

  $B$ : strength of the magnetic field

  $l$ : length of the wire

  $v$ : speed of charges.

  $B=\frac{F}{IL}\text{=}\left(\frac{\text{N}}{\text{A}\cdot \text{m}}\right)$

L is measured in $\text{m}$ and $v$ in $\text{m/s}$ .

  $EMF=Blv\left(\sin \theta \right)$ $\left(\frac{\text{N}}{\text{A}\cdot \text{m}}\right)\left(\text{m}\right)\left(\frac{\text{m}}{\text{s}}\right)\text{=}\left(\frac{\text{N}\cdot \text{m}}{\text{A}\cdot \text{s}}\right)\text{=}\frac{\text{J}}{\text{C}}\text{=V}$

Conclusion:

Hence, the unit substitution to show that the units of $Blv$ are in volts.