Electricity and Magnetism

Lenz's law

A square coil of resistance $2 \ \Omega,$ $80 \text{ turns}$ and side length $6 \text{ cm}$ is placed with its plane making an angle of $30^\circ$ with a uniform magnetic field of $\SI{3}{\tesla}.$ In $5.4 \text{ s}$ the coil rotates until its plane becomes parallel to the magnetic filed. Find the current induced in the coil.

A rectangular loop of sides $a = 3 \text{ cm}$ and $b = 6 \text{ cm}$ with a small break in it is moving out of a region of uniform magnetic field of $B = 0.3 \text{ T},$ directed normal to the loop. What is the emf developed across the break if the velocity of the loop is $v= 2 \text{ cm/s}$ in the direction normal to the longer side of the loop?

The magnetic flux through a coil of resistance $430 \ \Omega$ placed with its plane perpendicular to a uniform magnetic field varies with time $t \text{ (in seconds)}$ as $\Phi = (2 t^2 + 3 t + 4) \text{ mWb}.$ Find the induced current in the coil at $t = 10 \text{ s}.$

A solenoid of diameter $20 \text{ cm}$ has $50$ turns per meter. At the center of this solenoid, a coil of $5$ turns is wrapped closely around it. If the current in the solenoid changes from zero to $4 \text{ A}$ in $1 \text{ ms},$ what is the approximate induced emf developed in the coil?

A rectangular coil of $400$ turns and size $20 \text{ cm} \times 20 \text{ cm}$ is placed perpendicular to a magnetic field of $4 \text{ T}.$ Find the induced emf when the field drops to $2 \text{ T}$ in $1 \text{ s}.$

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