A solenoid has a cross-sectional area of$6.0 \times {10}^{–4} {\mathrm{m}}^2$consists of $400$ turns per meter, and carries a current of $0.40 \mathrm{A}$. A $10$ turn coil is wrapped tightly around the circumference of the solenoid. The ends of the coil are connected to a $1.5 \mathrm{\Omega }$ resistor. Suddenly, a switch is opened, and the current in the solenoid dies to zero in a time $0.050 \mathrm{s}$. Find the average current in the coil during this time.

Figure illustrates plane figures made of thin conductors which are located in a uniform magnetic field directed away from a reader beyond the plane of the drawing. The magnetic induction starts diminishing. Find how the currents induced in these loops are directed.

A uniform magnetic field B exists in a cylindrical region of radius $1 \mathrm{cm}$ as shown in figure. A uniform wire of length $16 \mathrm{cm}$and resistance $4.0 \mathrm{\Omega }$ is bent into a square frame and is placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of$1 \mathrm{T} {\mathrm{s}}^{-1}$, find the current induced in the frame.

Figure shows a square loop of resistance $1 \mathrm{\Omega }$ of side $1 \mathrm{m}$ being moved towards right at a constant speed of $1 \mathrm{m} {\mathrm{s}}^{-1}$.The front edge enters the $3 \mathrm{m}$ wide magnetic field$(\mathrm{B} = 1 \mathrm{T})$ at $\mathrm{t}=0$. Draw the graph of current induced in the loop as time passes. (Take anticlockwise direction of current as positive)

Figure shows a square loop of resistance $1 \mathrm{\Omega }$ of side $1 \mathrm{m}$ being moved towards right at a constant speed of $1 \mathrm{m} {\mathrm{s}}^{-1}$.The front edge enters the $3 \mathrm{m}$ wide magnetic field$(\mathrm{B} = 1 \mathrm{T})$ at $\mathrm{t}=0$. Draw the graph of current induced in the loop as time passes. (Take anticlockwise direction of current as positive)

A metallic wire $\mathrm{PQ}$ of length $1 \mathrm{cm}$ moves with a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$ in a direction perpendicular to its length and perpendicular to a uniform magnetic field of magnitude $0.2 \mathrm{T}$. Find the emf induced between the ends of the wire. Which end will be positively charged.