Question

For Eq. (29.6), show that if v is in meters per second, B in teslas, and L in meters, then the units of the right-hand side of the equation are joules per coulomb or volts (the correct SI units for E ).

Short answer

$$\begin{gathered} \mathrm{E}=\frac{\mathrm{J}}{\mathrm{C}} \\ =\mathrm{V} \end{gathered}$$

Step-by-step solution

Motional EMF

Motional EMF can be defined such an emf which induced by motion relative toa magnetic field.

Formula Motional EMF can be given by

E = BLv

Here, E is electric field, B is the magnetic field, L is the length, and v is the velocity.

 Calculation of units of EMF

E = BLv

Now put the units of constants in above relation

$$\begin{gathered} \mathrm{E}=\mathrm{T}.\mathrm{m}.\frac{\mathrm{m}}{\mathrm{s}} \\ =\frac{\mathrm{Ns}.\mathrm{m}.\mathrm{m}}{\mathrm{Cms}} \\ =\frac{\mathrm{N}.\mathrm{m}}{\mathrm{C}} \\ \mathrm{E}=\frac{\mathrm{J}}{\mathrm{C}} \\ =\mathrm{V} \end{gathered}$$

Hence, this is the unit of E.