Electromagnetic Induction

A uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of   $4\mathrm{m}\mathrm{m}$ and a total length of $30\mathrm{c}\mathrm{m}$ . The magnetic field changes with time at a steady rate $\frac{\mathrm{d}\mathrm{B}}{\mathrm{d}\mathrm{t}}=0.032{\mathrm{T}\mathrm{s}}^{-1}$   . The induced current in the loop is close to (Resistivity of the metal wire is $1.23*{10}^{-8}\mathrm{\Omega }\mathrm{m}$  )

An elliptical loop having resistance R, of semi major axis a and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency ω, the average power loss in the loop due to joule heating is:

A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 * 10⁻⁵ T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in V) in the coil will be close to the integer.

A part of complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of 10² As⁻¹. The value of the potential difference Vₚ - Vq, (in volts) at that instant, is

An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor $$ $\mathrm{C}$ with a sliding connector are located in the same plane, as shown in the figure. The connector has length I and resistance $R$ $$ . It slides to the right with a velocity $v$ $$ . The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation $r$ $$ , between the connector and the straight wire is:

Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $?$ $$ . The magnetic flux through the area is given by ${}_{}$ ${?}_0$ . Which of the following is correct?

At time $\mathrm{t}=0$ $$ magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next $5\mathrm{s}$ $$ , then induced EMF in the loops is:

A long solenoid of radius $R$ $$ carries a time ( $t)$ $$ dependent current ${}_{}$ $I\left(t\right)=I_{0}t(1-t)$ . A ring of radius $2R$ $$ is placed cordially near its middle. During the time internal $0\le t\le 1$ $$ , the induced current $\left(I_R\right)$ $\left({}_{}\right)$ and the induced $\mathrm{E}\mathrm{M}\mathrm{F}?\left(V_R\right)$ $\left({}_{}\right)$ in the ring changes as:

A planar loop of wire rotates in a uniform magnetic field. Initially, at $t=0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10\mathrm{s}$  about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at: