Name: Faraday’s Law of Induction and Lenz’s Law
Uploaded: 2019-07-19
Duration: 10 min 7 s
Description: Here is an interesting video on electromagnetic induction explaining Faraday's laws of induction and Lenz's law. Get in to it to understand more!

Question

Two circular loops, one of small radius

r

and other of larger radius

R

, such that

R > > r,

are placed coaxially with centres coinciding. Obtain the mutual inductance of the arrangement.

Accepted Answer

Let the current flowing through two concentric and coaxial coils be $I_{R}$ and $I_{r}$ as shown in the figure below.

The magnetic field at the centre of the outer coil due to the current flowing through it will be $B_{R} = \frac{μ_{\circ} I_{R}}{2 R}$ . As $R > > r$ , the magnetic field inside the coil with a smaller radius can be considered the same throughout the coil. Magnetic flux is the product of magnetic field and the area through which the flux passes. Hence, the flux linked with the coil with radius $r$ will be $φ_{r} = B_{R} π r^{2} = \frac{μ_{\circ} I_{R}}{2 R} \times π r^{2} = (\frac{μ_{\circ} π r^{2}}{2 R}) I_{R}$ ....(i)

Let the current flowing through the smaller coil be $I_{r}$ . Again considering the magnetic field within the smaller coil to be the same everywhere due to its smaller size, the magnetic flux linked with the larger coil, $φ_{R} = \frac{μ_{\circ} I_{r}}{2 R} \times π r^{2} = (\frac{μ_{\circ} π r^{2}}{2 R}) I_{r}$ ....(ii)

Using (i) and(ii), the mutual inductance of the two coils will be $(\frac{μ_{\circ} {πr}^{2}}{2 R})$ .

Two circular loops, one of small radius $r$ and other of larger radius $R$ , such that $R > > r,$ are placed coaxially with centres coinciding. Obtain the mutual inductance of the arrangement.

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !

Two circular loops, one of small radius r and other of larger radius R, such that R >> r, are placed coaxially with centres coinciding. Obtain the mutual inductance of the arrangement.

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !

Two circular loops, one of small radius $r$ and other of larger radius $R$ , such that $R > > r,$ are placed coaxially with centres coinciding. Obtain the mutual inductance of the arrangement.