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

Answer 2

The production of a potential difference in a coil due to magnetic flux is known as the induced emf. The average induced emf will be 0.00016391 V.

What is a magnetic field?

It is the type of field where the magnetic force is obtained. With the help of a magnetic field. The magnetic force is obtained it is the field felt around a moving electric charge.

(a) 0.00016391 V  is the average induced emf around the border of the circular region.

The given data in the problem is;

r is the  radius of horizontal circular region = 2.00 mm=0.002 m

$\rm B_i$ is the initial megnetic field=0T

$\rm B_f$ s the final megnetic field= 1.5 T

t  is the time taken= 115 ms0.115 sec

$\epsilon$ is the emf induced =?

The induced emf is found by;

$\epsilon = \frac{d \phi}{dt} \\\\ \epsilon = A\frac{B_f-B_i}{dt} \\\\ \epsilon = \pi r^2\frac{1.5-0}{0.115} \\\\ \epsilon = 0.00016391 \ V$

Hence  0.00016391 V  is the average induced emf around the border of the circular region.

(b) 0.00038665 V is the average induced emf around the border of the circular region over this time period.

The given data in the problem is;

r is the  radius of horizontal circular region = 2.00 mm,

$\rm B_i$ is the initial megnetic field=+1.5 T

$\rm B_f$ s the final megnetic field= -1.5 T

t  is the time taken= 65 ms=0.065 sec

$\epsilon$ is the emf induced =?

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

Hence 0.00038665 V is the average induced emf around the border of the circular region over this time period.

To learn more about the magnetic field refer to the link;

https://brainly.com/question/19542022