Electromagnetic Induction

A coil of effective area $3$ m$^2$ is placed at right angles to a magnetic field of induction $0.05$ Wb/m$^2$. If the field is decreased to $20\%$ of its original value in $10$ second, the e.m.f. induced in the coil will be

The self inductance of an air-core inductor (solenoid) is $0.03$ mH. By introducing an iron core into inductor the self-inductance increases to $30$ mH. The relative permeability of the core used is

An aeroplane having a wing span of 30 m flies due north with the speed of 170 m/s. Magnetic field $B = 3.6 \times 10^{-5}$ T. The potential difference between the tips of the wings will be

A circular disc of radius 20 cm is placed in uniform magnetic field of induction $\dfrac{7}{22}\ \text{Wb/m}^2$ in such a way that its axis makes an angle of $60^\circ$ with $\vec{B}$. The magnetic flux linked with the disc is $(\cos 60^\ci...

Magnetic flux linked with the coil in weber is given by the equation $\Phi = 5t^2 + 6t + 11$. The e.m.f. induced in the coil in the $5^{\text{th}}$ second will be

Consider two coils in which a current in one coil carrying $6$ A causes the change in the flux in the second coil $12 \times 10^{-4}$ weber/turn. The second coil has $2000$ turns. The mutual inductance between the coils is

Two different coils have self-inductance $3L$ and $L$. The current in both the coils is increased at the same constant rate. At certain instant of time, the power given to the two coils is same. At that time there was current and voltage in...

The magnetic energy stored in an inductor of inductance $4\,\text{H}$ carrying a current of $1.5$ A is

A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, then the current in the coil

The magnetic potential energy stored in a certain inductor is $49\ \text{mJ}$ when the current in the inductor is $70\ \text{mA}$. The inductance of the inductor is

Two coils have a mutual inductance of $0.005\ \text{H}$. The current changes in the first coil according to equation $I = I_0\sin\omega t$, where $I_0 = 10\ \text{A}$ and $\omega = 60\pi\ \text{rad s}^{-1}$. The maximum values of e.m.f. in ...

In the circuit shown, when the current '$i$' is $3\text{A}$ and increasing at the rate of $1\text{A/s}$ the measurement of the potential difference between A and B is $12\ \text{V}$. But when the same current $3\text{A}$ is decreasing at th...

The equivalent inductance between A and B is equal to

If current of 4 A produces magnetic flux of $3 \times 10^{-3}$ Wb through a coil of 400 turns, the energy stored in the coil will be

Two coils A and B have 180 and 360 turns respectively. The current of 1A flows through both the coils. Due to current of 1A in coil A, flux per turn of $0.8 \times 10^{-3}$ Wb is linked with coil A. Due to current of 1A in coil B, flux per ...

Two coils have self inductance $L_1$ and $L_2$. The current through them is increasing at constant rate. If the power dissipated in both the coils is same, then the ratio of energy stored in the coil having inductance $L_1$ to that in $L_2$...

Three coils of inductance, $L_1$ = 2 H, $L_2$ = 3 H and $L_3$ = 6 H are connected so that they are separated from each other. To obtain the effective inductance of $\dfrac{18}{11}$ H between points A and B, out of the following figures, the...

A straight line conductor of length 0.4 m is moved with a speed of $7.0 \text{ ms}^{-1}$ perpendicular to magnetic field of intensity $0.8 \text{ Wb m}^{-2}$. The induced e.m.f. across the conductor is

Two coils having self-inductance $L_1 = 75$ mH and $L_2 = 48$ mH are coupled with each other. If the mutual inductance of the coils is 37.2 mH, then coefficient of coupling will be

Two planar concentric rings of metal wire having radii '$r_1$' and '$r_2$' (with $r_1 > r_2$) are placed in air. The current 'I' is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( $\mu_0$ = p...

A metal rod of length 'L' completes the circuit as shown. The area of the circuit is perpendicular to magnetic field 'B'. Total resistance of the circuit is 'R'. The force needed to move the rod in the direction as shown with constant speed...

In the given circuit, if $dI/dt = -1\ \text{A/s}$ then the value of $V_{AB}$ at this instant will be

A graph of magnetic flux ($\Phi$) versus current (I) is shown for four inductors A, B, C, D. The smallest value of self inductance is for inductor.

A circular coil of radius 'r' is placed on another circular coil whose radius is 'R' and the current flowing through it is changing and their centers coincide. ($R \gg r$). If both the coils are coplanar, then the mutual inductance between ...

A bar magnet falls from a height 'h' through a metal pipe, its acceleration after coming out of pipe is

The coefficient of mutual induction is $3$H and induced e.m.f. across secondary is $4$ kV. Current in primary is reduced from $7$A to $2$A. The time required for the change of current is

A coil of 'n' turns and resistance $R\,\Omega$ is connected in series with a resistance $R/4$. The combination is moved for time 't' second through flux $\Phi_1$ to $\Phi_2$. The induced current in the circuit is

Two solenoids A and B of equal number of turns have their lengths and radii in the same ratio $1 : 3$. The ratio of the self-inductance of solenoid A to that of B will be

Two concentric circular coils having radii $r_1$ and $r_2$ ($r_2 << r_1$) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

Two coils P and Q have mutual inductance 'M' H. If the current in the coil P is $I = I_0 \sin \omega t$, then the maximum value of e.m.f. induced in coil Q is

The current flowing through the inductor of self inductance 'L' is continuously increasing at constant rate. The variation of induced e.m.f. (e) versus $\dfrac{dI}{dt}$ is shown graphically by figure

A conducting loop of radius $10/[\pi]^{1/2}$ cm is placed perpendicular to a uniform magnetic field $0.5$ T. The magnetic field is decreased to zero in $0.5$ s at a steady rate. The induced emf in the circular loop at $0.25$ s is

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}

The following figure represents two bulbs $B_1$ and $B_2$, resistor R and an inductor L. When the switch S is turned off, which of the following statement is true?

A long rectangular conducting loop of width '$l$' mass '$m$' and resistance '$R$' is placed partly in a perpendicular magnetic field '$B$'. With what velocity should it be pushed downwards so that it may continue to fall without any acceler...

A square loop of area $25 \text{ cm}^2$ has a resistance of $10$ $\Omega$. The loop is placed in uniform magnetic field of magnitude $40$ T. The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out...

Alternating current of peak value $\left(\dfrac{2}{\pi}\right)$ A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is $1$ H. The peak em.f. induced in secondary coil i...

A coil having 'n' turns and resistance 'R' is connected with a galvanometer of resistance '2R'. This combination is moved in time 't' from flux $\phi_1$ to $\phi_2$ Wb. The induced current in the circuit is

A coil having ' $N$ ' turns and resistance ' $R$ ' $\Omega$ is connected to a galvanometer of resistance ' 6 R ' $\Omega$. The magnetic flux linked with this coil changes from $\phi_1$ weber to $\phi_2$ weber in time ' t ' second. The induc...

Two inductors of 80 mH each are joined in parallel. The current passing through the combination is 2.1 A . The energy stored in this combination of inductors is

A coil of effective area $3 \mathrm{~m}^2$ is placed at right angles to a magnetic field of induction $0.05 \mathrm{~Wb} / \mathrm{m}^2$ If the field is decreased to $20 \%$ of its original value in 10 second, the e.m.f. induced in the coil...

Two circuits A and B are connected to identical d.c. sources each of e.m.f. 10 volt. Self-inductances of circuits A and B are respectively $\mathrm{L}_{\mathrm{A}}=10 \mathrm{H}$ and $\mathrm{L}_{\mathrm{B}}=10 \mathrm{mH}$. The total resis...

A magnetic field $4 \times 10^{-2} \mathrm{~T}$ acts at right angles to a coil of area $100 \mathrm{~cm}^2$ with 50 turns. The average e.m.f. induced in the coil is 0.1 V , when it is removed from the field in time ' $t$ '. The value of ' $...

When magnetic flux changes from $6.5 \times 10^{-2} \mathrm{~Wb}$ to $11 \times 10^{-2} \mathrm{~Wb}$ and the change in current is 0.03 A , the coefficient of mutual inductance will be

The plot of magnetic flux ' $\phi$ ' linked with the coil versus current ' I ' is as shown in figure for two inductors $\mathrm{L}_1$ and $\mathrm{L}_2$. The self inductance of

A long rectangular conducting loop of width ' $l$ ', mass ' $m$ ' and resistance ' $R$ ' is placed partly in a perpendicular magnetic field ' B '. It is pushed downwards with velocity ' $V$ ' so that it may continue to fall freely. The velo...

Two coils P and Q are kept near each other. When no current flows through coil P and current increases in coil Q at the rate $10 \mathrm{~A} / \mathrm{s}$, the emf in coil P is 12 mV . When coil Q carries no current and current of 1.5 A flo...

The equivalent inductance between A and B is equal to

A copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ( $\ma...

A coil of ' $n$ ' turns and resistance $R \Omega$ is connected in series with a resistance $\frac{R}{2}$. The combination is moved for time ' $t$ ' second through magnetic flux $\phi_1$ to $\phi_2$. The induced current in the circuit is