Karnataka Board Solutions for Chapter: Electromagnetic Induction, Exercise 1: EXERCISES

Use Lenz’s law to determine the direction of induced current in the situations described by the following figure:

A circular loop being deformed into a narrow straight wire.

A rectangular wire loop of sides $8 \mathrm{c}\mathrm{m}$ and $2 \mathrm{c}\mathrm{m}$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3 \mathrm{T}$ directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is $1 \mathrm{c}\mathrm{m}{\mathrm{s}}^{–1}$ in a direction normal to the shorter side of the loop? For how long does the induced voltage last in this case?

A $1.0 \mathrm{m}$ long metallic rod is rotated with an angular frequency of $400 \mathrm{r}\mathrm{a}\mathrm{d} {\mathrm{s}}^{–1}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of $0.5 \mathrm{T}$ parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring

A circular coil of radius $8.0 \mathrm{c}\mathrm{m}$ and $20$ turns is rotated about its vertical diameter with an angular speed of $50 \mathrm{r}\mathrm{a}\mathrm{d} {\mathrm{s}}^{–1}$ in a uniform horizontal magnetic field of magnitude $3.0\times {10}^{–2} \mathrm{T}$. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance $10 \mathrm{\Omega }$, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

A horizontal straight wire $10 \mathrm{m}$ long extending from east to west is falling with a speed of $5.0 \mathrm{m}{\mathrm{s}}^{–1}$, at right angles to the horizontal component of the earth’s magnetic field. a) What is the instantaneous value of the emf induced in the wire? (b) What is the direction of emf? c) Which end of the wire is at the higher electrical potential?

Current in a circuit falls from $5.0 \mathrm{A}$ to $0.0 \mathrm{A}$ in $0.1 \mathrm{s}$. If an average emf of $200 \mathrm{V}$ induced, give an estimate of the self-inductance of the circuit.

A pair of adjacent coils has a mutual inductance of $1.5 \mathrm{H}$. If the current in one coil changes from $0$ to $20 \mathrm{A}$ in $0.5 \mathrm{s}$, what is the change of flux linkage with the other coil?

A jet plane is travelling towards west at a speed of $1800 \mathrm{k}\mathrm{m}/\mathrm{h}$. What is the voltage difference developed between the ends of the wing having a span of $25 \mathrm{m}$, if the Earth’s magnetic field at the location has a magnitude of $5\times {10}^{–4} \mathrm{T}$ and the dip angle is $30°.$