Faraday's Law

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?

(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

Find the magnitude of magnetic flux through the circular loop at $t=t$

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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.

Magnetic flux linked with a stationary loop of resistance $4 \mathrm{\Omega }$ varies with time as $\varphi =3t\left(2-t\right)$. (In Wb). The amount of heat generated in joules during $t=0$ to $t=2 \mathrm{s}$ is

A metallic horizontal ring of mass $m$ and radius $r$ falling under gravity in a region having magnetic field. If $z$ is the vertical direction, the $z$-component of magnetic field is $B_0(1+az)$ where $B_0$ and a are constants. If $R$ is the resistance of the ring, the terminal velocity of the ring is

The S.I. unit of magnetic field intensity is

A square loop of side $a$ lies in the $x-y$ plane with its sides parallel to the axes. It is moved into a region of magnetic field with a constant velocity $\overrightarrow{v}$ in the $x$-direction. The magnetic field in one region of width$a$ is given by $\overrightarrow{B}=B_0\hat{k}$ and in an adjacent region, also of width $a$, the magnetic field is $\overrightarrow{B}=-B_0\hat{k}$

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Which of the following graphs shows the emf induced in the loop as it enters the field region and finally leaves it? In these graphs $E_0=B_{0}av$.

A dynamo converts

When the current in a coil changes from $5 \mathrm{A}$ to $2 \mathrm{A}$ in $\mathrm{0}.1 \mathrm{s}$, an average voltage of $\mathrm{50\hspace{0.17em}}\mathrm{V}$ is produced. The self-inductance of the coil is

Will the earth’s magnetic field induce any current in the metallic surface of an artificial satellite when it is orbiting around the poles?

Magnetic flux is the product of magnetic field induction and area.

A circuit consists of a coil with inductance $L$ and an uncharged capacitor of capacitance $C$. The coil is in a constant uniform magnetic field such that the flux through the coil is $\varphi$. At time $t=0 \min$, the magnetic field is abruptly switched OFF. Let ${\omega }_0=1/\sqrt{LC}$ and ignore the resistance of the circuit. Then,

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($\theta$)

A square coil of $0.01 {\mathrm{m}}^2$ area is placed perpendicular to the uniform magnetic field of intensity ${10}^3 {\mathrm{Wbm}}^{-2}$. The magnetic flux (in weber) linked with the coil is

A circuit consists of a coil with inductance $L$ and an uncharged capacitor of capacitance $C$. The coil is in a constant uniform magnetic field such that the flux through the coil is $\varphi$. At time $t=0 \min$, the magnetic field is abruptly switched OFF. Let ${\omega }_0=\frac{1}{\sqrt{LC}}$ and ignore the resistance of the circuit. Then,

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 law of electromagnetic induction has been used in the construction of