finding magnitude and direction of induced currents Hw3 5 A

finding magnitude and direction of induced currents

Hw3 #5 A curernt lo magnetic field B(t) as shown below op (the length is a and the height is b, the resistance is R) is located in a time-dependent Find the magnitude and the direction of the induced current in the loop for two cases: a) B(t) = Bo + at, b) B(t) = Bo-ot, where Bo and are constants.

Solution

a) Magnetic flux through the loop,

= BA = (B_o + t)(ab) = abB_o + abt

Magnitude of induced emf, E = |d/dt| = ab

Magnitude of induced current, I = E/R = ab/R

Since the magnetic field is increasing, the magnetic flux through the loop is increasing. So, the magnetic field due to the induced current should be out of the page. Hence, the direction of induced current is clockwise.

b) Magnetic flux through the loop,

= BA = (B_o - t)(ab) = abB_o - abt

Magnitude of induced emf, E = |d/dt| = ab

Magnitude of induced current, I = E/R = ab/R

Since the magnetic field is decreasing, the magnetic flux through the loop is decreasing. So, the magnetic field due to the induced current should be into the page. Hence, the direction of induced current is anticlockwise.