Maharashtra Board Solutions for Chapter: Electromagnetic Induction, Exercise 4: Exercises

Two inductor coils with inductance $10 \mathrm{mH}$ and $20 \mathrm{mH}$ are connected in series. What is the resultant inductance of the combination of the two coils?

Calculate the value of induced emf between the ends of an axle of a railway carriage $1.75 \mathrm{m}$ long travelling on level ground with a uniform velocity of $50 \mathrm{km}$ per hour. The vertical component of Earth’s magnetic field ($\mathrm{B}$) is given to be $5\times {10}^{-5}\mathrm{T}$.

The value of mutual inductance of two coils is $10 \mathrm{mH}$. If the current in one of the coil changes from $5\mathrm{A}$ to $1\mathrm{A}$ in $0.2 \mathrm{s}$, calculate the value of emf induced in the other coil.

An emf of $96.0 \mathrm{mV}$ is induced in the windings of a coil when the current in a nearby coil is increasing at the rate of $1.20 \mathrm{A}/\mathrm{s}$. “What is the mutual inductance ($\mathrm{M}$) of the two coils?

A long solenoid of length $\mathrm{l}$, cross- sectional area $\mathrm{A}$ and having ${\mathrm{N}}_1$ turns (primary coil) has a small coil of ${\mathrm{N}}_2$, turns (secondary coil) wound about its centre. Determine the Mutual inductance ($\mathrm{M}$) of the two coils.

The primary and secondary coil of a transformer each have an inductance of $200\times {10}^{-6} \mathrm{H}$. The mutual inductance ($\mathrm{M}$) between the windings is $4\times {10}^{-6} \mathrm{H}$. What percentage of the flux from one coil reaches the other’?

A toroidal ring, having $100$ turns per $\mathrm{cm}$ of a thin wire is wound on a non- magnetic metal rod of length $1 \mathrm{m}$ and diameter $1 \mathrm{cm}$. If the permeability of bar is equal to that of free space (${\mu }_0$), calculate the magnetic field inside the bar ($\mathrm{B}$) when the current ($\mathrm{I}$) circulating through the turns is $1 \mathrm{A}$. Also determine the self-inductance ($\mathrm{L}$) of the coil.

A uniform magnetic field $\mathrm{B}\left(\mathrm{t}\right)$, pointing upward fills a circular region of radius, $\mathrm{s}$ in a horizontal plane. If $\mathrm{B}$ is changes with time, find the induced electric field.