Faraday's Laws of Induction

The magnetic flux through each of five faces of a neutral playing dice is given ${\mathrm{\varphi }}_{\text{B}}=\pm \text{NWb}$, where N (= 1 to 5) is the number of spots on the face. The flux is positive (out-ward) for N even and negative (inward) for N odd. What is the flux through the sixth face of the die?

According to Faraday’s law of electromagnetic induction:

A rectangular loop and a circular loop are moving out of a uniform magnetic field to a field – free region with a constant velocity ‘v’ as shown in the figure. Explain which loop do you expect the induced emf to be constant during the passage out of the field region. The magnetic field is normal to the loops.

(i) In an a.c. generator, coil of $N$ turns and area $A$ is rotated at $v$ revolution per second in a uniform magnetic field $B$. Write the expression for the emf produced.

(ii) A $100$ turn coil of area  $0.1{\text{ m}}^{\text{2}}$  rotates at half a revolution per second. It is placed in a magnetic field $0.01 \mathrm{T}$ perpendicular to the axis of rotation of the coil. Calculate the maximum voltage generated in the coil.

The dimensional formula of magnetic flux is

A coil of an area $2 {\mathrm{m}}^2$ is placed in a magnetic field which changes from $4 \mathrm{Wb}/{\mathrm{m}}^2$ to $8 \mathrm{Wb}/{\mathrm{m}}^2$ in $2$ seconds. Find the induced e.m.f. in the coil.

If the magnitude of emf induced across a coil is given by $\epsilon =4t \mathrm{V}$ where $t$ is time in second then the best possible graph for the variation of flux versus time is (Given flux through coil is zero at $t=0$)

A wire, bent into the shape of a right angled triangle $PQR$, lies with its side $PQ$ parallel to a current carrying wire, and side $QR$ perpendicular to it. The loop lies in the plane of the wire. EMF induced in the loop when it is moved with constant speed along $PR$ is ${\epsilon }_1$ and it is ${\epsilon }_2$ when moved along $QR$ with the same constant speed. Then,

The S.I. unit of magnetic field intensity is

A loop having resistance $R$ and in the shape of equilateral triangle has sides $1 \mathrm{m}$ is placed in a perpendicular magnetic field which is varying at $\frac{\mathrm{d}B}{\mathrm{d}t}=1 \mathrm{T} {\mathrm{s}}^{-1}$. The induced current in the loop will be

A coil has $200\mathrm{ }\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{s}$ and area of $70\mathrm{ }{\mathrm{c}\mathrm{m}}^2$. The magnetic field perpendicular to the plane of the coil is $0.3\mathrm{ }\mathrm{W}\mathrm{b}/{\mathrm{m}}^2$ and take $0.1\mathrm{ }\mathrm{s}\mathrm{e}\mathrm{c}$ to rotate through $180°$. The value of the induced e.m.f. will be -

A dynamo converts

The law that states “The induced e.m.f. is proportional to the rate of change of its number of lines of magnetic force linking the circuit” is

Which one is the correct relation between magnetic flux $\left(\varphi \right)$. magnetic field $\left(B\right)$, area surface $A$ and angle between the magnetic field lines and perpendicular distance normal to the surface area($\theta$)

If a coil of metal wire is kept stationary in a uniform magnetic field, then _____.

Which of the following operations between the magnetic field and the area gives the magnetic flux?

The magnetic flux linked (in Weber) with a coil of resistance $10 \mathrm{\Omega }$ is varying with respect to time $t$ as $\Phi =4t^2+2t+1$. Then the current in the coil at time $t=1$ second is

The law of electromagnetic induction has been used in the construction of

Whenever a magnet is moved either towards or away from a conducting coil. An emf is induced then the magnitude of induced emf is independent of

In an AC dynamo, the peak value of emf is $60 \mathrm{V}$. The induced emf, in a position when perpendicular to the armature coil making an angle of ${30}^{\circ }$ with the magnetic field, will be