Faraday's Law of Electromagnetic 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.

A rectangular frame $ABCD$ made of a uniform metal wire has a straight connection between $E$ and $F$ made of the same wire as shown in the figure. $AEFD$ is a square of side $1 \mathrm{m}$ and $EF=FC=0.5 \mathrm{m}$. The entire circuit is placed in a steadily increasing uniform magnetic field directed into the plane of the paper and normal to it. The rate of change of the magnetic field is $1 \mathrm{T} {\mathrm{s}}^{-1}$, the resistance per unit length of the wire is $1 \mathrm{\Omega } {\mathrm{m}}^{-1}$.  If the current in segments $BE$ is $\frac{x}{22} \mathrm{A}$, find $x$.

A ring of mass m, radius r having charge q uniformly distributed over it and free to rotate about it's own axis is placed in a region having a magnetic field B parallel to its axis. If the magnetic field is suddenly switched off, the angular velocity acquired by the ring is   

A circular loop of radius $r$ is moved with a velocity $v$ as shown in the diagram. The work needed to maintain its velocity constant is: (wire is infinitely long)

A square wire frame of side a is placed a distance b away from a long straight conductor carrying current I. The frame has resistance R and self-inductance L. The frame is rotated by ${180}^{\mathrm{o}}$ about OO' as shown in Fig. Find the electric charge flown through the frame -

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

A conducting ring of circular cross-section with inner and outer radii $\mathrm{a}$ and $\mathrm{b}$ is made out of a material of resistivity $\mathrm{\rho }$. The thickness of the ring is $\mathrm{h}$. It is placed coaxially in a vertical cylindrical region of a magnetic field $\mathrm{B}=\mathrm{krt}$, where $\mathrm{k}$ is a positive constant, $\mathrm{r}$ is the distance from the axis and $\mathrm{t}$ is the time. If the current through the ring is $\mathrm{I}=\left(\frac{\mathrm{kh}}{\alpha \rho }\right)\mathrm{ }\left[{\mathrm{b}}^3-{\mathrm{a}}^3\right]$, then what is the value of $\mathrm{\alpha }$?
 

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,

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 conducting ring of circular cross-section with inner and outer radii $\mathrm{a}$ and $\mathrm{b}$ is made out of a material of resistivity $\mathrm{\rho }$. The thickness of the ring is $\mathrm{h}$. It is placed coaxially in a vertical cylindrical region of a magnetic field $\mathrm{B}=\mathrm{krt}$, where $\mathrm{k}$ is a positive constant, $\mathrm{r}$ is the distance from the axis and $\mathrm{t}$ is the time. If the current through the ring is $\mathrm{I}=\left(\frac{\mathrm{kh}}{\mathrm{\alpha p}}\right)\mathrm{ }\left[{\mathrm{b}}^3-{\mathrm{a}}^3\right]$, then what is the value of $\mathrm{\alpha }$?
 

A loop ABCDEFA of straight edges has six corner points $A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0),$ $\mathrm{E}(0, 5, 5)$ and $F(0, 0, 5)$. The magnetic field in this region is $\overrightarrow{B}=\left(3\hat{i}+4\hat{k}\right) \mathrm{T}$. The quantity of flux through the loop ABCDEFA (in $\mathrm{Wb}$) is

Imagine a world where free magnetic charges exist. In this world, a circuit is made with a $U$ shape wire and a rod free to slide on it. A current carried by free magnetic charges can flow in the circuit. When the circuit is placed in a uniform electric field, $E$ perpendicular to the plane (inward) of the circuit and the rod is pulled to the right with a constant speed $v,$ the "magnetic EMF" in the current and the direction of the corresponding current, arising because of changing electric flux will be ($l$ is the length of the rod and $c$ is speed of light ).

A conducting ring of circular cross-section with inner and outer radii $\mathrm{a}$ and $\mathrm{b}$ is made out of a material of resistivity $\mathrm{\rho }$. The thickness of the ring is $\mathrm{h}$. It is placed coaxially in a vertical cylindrical region of a magnetic field $\mathrm{B}=\mathrm{krt}$, where $\mathrm{k}$ is a positive constant, $\mathrm{r}$ is the distance from the axis and $\mathrm{t}$ is the time. If the current through the ring is $\mathrm{I}=\left(\frac{\mathrm{kh}}{\alpha \rho }\right)\mathrm{ }\left[{\mathrm{b}}^3-{\mathrm{a}}^3\right]$, then what is the value of $\mathrm{\alpha }$?
 

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($\theta$)

Imagine a world where free magnetic charges exist. In this world, a circuit is made with a $U$ shape wire and a rod free to slide on it. A current carried by free magnetic charges can flow in the circuit. When the circuit is placed in a uniform electric field, $E$ perpendicular to the plane of the circuit and the rod is pulled to the right with a constant speed $v,$ the "magnetic EMF" in the current and the direction of the corresponding current, arising because of changing electric flux will be ($l$ is the length of the rod and $c$ is speed of light ).

A conducting rod, with a resistor of resistance $R,$ is pulled with constant speed $v$ on a smooth conducting rail as shown in figure. A constant magnetic field $\overrightarrow{B}$ is directed into the page. If the speed of the bar is doubled, by what factor does the rate of heat dissipation across the resistance $R$ change?