Electromagnetic...

Magnetic flux linked with a stationary loop resistance $$R$$ varies with respect to time during the time period $$T$$ as follows:
$$\phi=at(T-t)$$
The amount of heat generated in the loop during that time (inductance of the coil is negligible) is

In the figure, there exists a uniform magnetic field $$B$$ into the plane of paper. Wire $$CD$$ is in the shape of an arc and is fixed. $$OA$$ and $$OB$$ are the wires rotating with angular velocity $$\omega$$ as shown in the figure in the same plane as that of the arc about point $$O$$. If at some instant, $$OA=OB=1$$ and each wire makes angle $$\theta={30}^{o}$$ with y-axis, then the current through resistance $$R$$ is (wire $$OA$$ and $$OB$$ have no resistance)

The current through the coil in figure (i) varies as shown in figure (ii). Which graph best shows ammeter $$A$$ reading as a function of time?

A conducting ring of radius $$r$$ is rolling without slipping with a constant angular velocity $$\omega$$ (figure). If the magnetic field strength is $$B$$ and is directed into the page then the emf induced across $$PQ$$ is

A rectangular loop with a sliding conductor of length $$l$$ is located in a uniform magnetic field perpendicular to the plane of the loop (figure). The magnetic induction is $$B$$. The conductor has a resistance $$R$$. The sides $$AB$$ and $$CD$$ have resistances $${R}_{1}$$ and $${R}_{2}$$ respectively. Find the current through the conductor during its motion to the right with a constant velocity $$v$$.

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 figure. $$AEFD$$ is a square of side $$1m$$ and $$EB=FC=0.5m$$. The entire circuit is placed in a steadily increasing, uniform magnetic field directed into the plane of paper and normal to it. The rate of change of the magnetic field is $$1$$ $$T{s}^{-1}$$. The resistance per unit length of the wire is $$1\Omega$$ $${m}^{-1}$$. Find the magnitude and direction of the current in the segment $$AE$$, $$BE$$ and $$EF$$.

In the circuit shown in figure, a conducting wire $$HE$$ is moved with a constant speed $$v$$ toward left. The complete circuit is placed in a uniform magnetic field $$\vec { B } $$ perpendicular to the plane of the circuit inward. The current in $$HKDE$$ is 

A conducting rod $$PQ$$ of length $$l=2m$$ is moving at a speed of $$2m$$ $${s}^{-1}$$ making an angle of $${30}^{o}$$ with its length. A uniform magnetic field $$B=2T$$ exists in a direction perpendicular to the plane of motion. Then

Two identical conducting rings $$A$$ and $$B$$ of radius $$R$$ are rolling over a horizontal conducting plane with same speed $$v$$ but in opposite direction. A constant magnetic field $$B$$ is present pointing into the plane of the paper. Then the potential difference between the highest points of the two rings is

A rod of length $$L$$ rotates in the form of a conical pendulum with an angular velocity $$\omega$$ about its axis as shown in figure. The rod makes an angle $$\theta$$ with the axis. The magnitude of the motional emf developed across the two ends of the rod is