Question

Two coils have mutual inductance $M=3.25\times {10}^{-4}H$. The current in the first coil increases at a uniform rate of 830 A/S. (a) what is the magnitude of the induced emf in the second coil? Is it constant? (b) Suppose that the current described is in the second coil rather than the first. What is the magnitude of the induced emf in the first coil?

Short answer

Answer

(a) The magnitude of induced emf in the second coil is 0.270 V which is constant.

(b) The magnitude of induced emf in the first coil is 0.270 V.

Step-by-step solution

Define mutual inductance and its formula

When changing current in one circuit changes the magnetic flux in other circuit, an emf is induced in the latter circuit. This emf is directly proportional to the time rate of current in former circuit. The constant so introduced removing the proportionality is called mutual inductance.

${\mathit{\epsilon }}_{\mathbf{2}}\mathbf{=}\mathbf{-}\mathit{M}\frac{\mathbf{d}{\mathbf{i}}_{\mathbf{1}}}{\mathbf{d}\mathbf{t}}$

Where, is the induced emf in second circuit, $\frac{d{i}_1}{dt}$is the time rate of current flowing in first circuit and is the mutual inductance.

Calculation using formula

(a)

Two coils have mutual inductance $M=3.25\times {10}^{-4}H$. The current in the first coil increases at a uniform rate of$\frac{d{i}_1}{dt}=830A/s$.

Magnitude of induced emf in second coil,

role="math" $\left|{\epsilon }_2\right|=M\frac{d{i}_1}{dt}$

$$\begin{gathered} {\epsilon }_2=3.25\times {10}^{-4}\times 830V \\ {\epsilon }_2=0.270V \end{gathered}$$

Thus, the magnitude of induced emf in second coil is which is constant.

(b)

Suppose that the current described is in the second coil rather than the first then$\frac{d{i}_2}{dt}=830A/s$ .

Magnitude of induced emf in first coil,

$$\begin{gathered} \left|{\epsilon }_1\right|=M\frac{d{i}_2}{dt} \\ {\epsilon }_1=3.25\times {10}^{-4}\times 830V \\ {\epsilon }_1=0.270V\backslash \mathrm{hfill} \end{gathered}$$

Thus, the magnitude of induced emf in first coil is 0.270 V.