Chapter 26, Problem 55A

To determine

To Show: The units of $\frac{E}{B}$ are the same as the units for velocity.

Answer to Problem 55A

The unit of $\frac{E}{B}$ is same as unit of velocity.

Explanation of Solution

Introduction:

The unit of magnetic field is denoted as Tesla or ${\text{Wb/m}}^{\text{2}}$ (SI unit). On the other hand, SI unit of electric field is V/m. unit of velocity is m/s.

We know that electric field is given by

  $E=\frac{F}{q}$  ...... (1)

Here $F$ is the force, $q$ is the charge and $E$ is the electric field.

Now we know that force experience by a charge particle in present of magnetic field is

  $F=qvB$  ...... (2)

Here $F$ is the force experience by a charge particle, $q$ is the charge, $v$ is velocity of the particle and $B$ is the applied magnetic field.

From (1) and (2) ,

  $\begin{array}{c}Eq=qvB\\ E=vB\end{array}$

  $v=\frac{E}{B}$  ...... (3)

Substitute $\text{V/m}$ as a unit for $E$ and ${\text{Wb/m}}^{\text{2}}$ as a unit for $B$ in equation (3)

  $\begin{array}{c}v=\frac{\text{V/m}}{{\text{Wb/m}}^{\text{2}}}\\ v=\text{m/s}\end{array}$

This is the unit of velocity.

Conclusion:

Hence, the unit of $\frac{E}{B}$ is same as unit of velocity.