Electricity and Magnetism

Magnetic Flux, Induction, and Ampere's Circuital Law

Lenz's law


A square coil of resistance 2 Ω, 2 \ \Omega, 80 turns 80 \text{ turns} and side length 6 cm 6 \text{ cm} is placed with its plane making an angle of 30 30^\circ with a uniform magnetic field of 3 T.\SI{3}{\tesla}. In 5.4 s 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 cm a = 3 \text{ cm} and b=6 cm b = 6 \text{ cm} with a small break in it is moving out of a region of uniform magnetic field of B=0.3 T, 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 cm/s 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 Ω 430 \ \Omega placed with its plane perpendicular to a uniform magnetic field varies with time t (in seconds) t \text{ (in seconds)} as Φ=(2t2+3t+4) mWb. \Phi = (2 t^2 + 3 t + 4) \text{ mWb}. Find the induced current in the coil at t=10 s. t = 10 \text{ s}.

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

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


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