Question

A magnetic field is uniform over a flat, horizontal circular region with a radius of 2.00 mm, and the field varies with time. Initially the field is zero and then changes to 1.50 T, pointing upward when viewed from above, perpendicular to the circular plane, in a time of 115 ms.
(a) what is the average induced emf around the border of the circular region? (Enter the magnitude in μν and the direction as seen from above.) magnitude direction Selet as seen from above
(b) Immediately after this, in the next 65.0 ms, the magnetic field changes to a magnitude of 0.500 T, pointing downward when viewed from above. What is the average induced emf around the border of the circular region over this time period? (Enter the magnitude in uv and the direction as seen from above.) magnitude direction cas seen from above.

Answer 1

Answer:

0.00016391 V

0.00038665 V

Explanation:

r = Radius = 2 mm

$B_i$ = Initial magnetic field = 0

$B_f$ = Final magnetic field = 1.5 T

t = Time taken = 115 ms

Induced emf is given by

$\varepsilon=\frac{d\phi}{dt}\\\Rightarrow \varepsilon=\frac{A(B_f-B_i)}{dt}\\\Rightarrow \varepsilon=\frac{\pi 0.002^2(1.5)}{0.115}\\\Rightarrow \varepsilon=0.00016391\ V$

The magnitude of the induced emf is 0.00016391 V

$B_i=+1.5\ T$

$B_f=-0.5\ T$

t = 65 ms

$\varepsilon=\frac{d\phi}{dt}\\\Rightarrow \varepsilon=\frac{A(B_f-B_i)}{dt}\\\Rightarrow \varepsilon=\frac{\pi 0.002^2(-0.5-1.5)}{0.065}\\\Rightarrow \varepsilon=-0.00038665\ V$

The magnitude of the induced emf is 0.00038665 V