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Electricity and Magnetism

Magnetic Flux, Induction, and Ampere's Circuital Law

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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