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Magnetic Flux, Induction, and Ampere's Circuital Law

Magnetic fields are wondrous things, bound by geometric relationships to the moving currents that generate them. Learn these links and the things they govern, from transformers to electric motors.

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 \( 3 \text{ T}. \) 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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