Question

A circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.064 T. The plane of the loop is perpendicular to the direction of the magnetic field. In a time interval of 0.46 s, the magnetic field changes to the opposite direction with a magnitude of 0.043 T. What is the magnitude of the average emf induced in the loop

Answer 1

Answer:

The magnitude of average induced emf = 0.229 mV

Explanation:

Given :

Radius of circular loop $r = 4 \times 10^{-2}$ m

Initial magnetic field $B_{1} = 0.064$ T

Final magnetic field $B_{2} = 0.043$ T

Difference of magnetic field $\Delta B = B_{1} - B_{2} = 0.021$

Time interval $\Delta t = 0.46$ sec.

According to the theory of electromagnetic induction,

Average emf =  $\frac{- \Delta \phi}{\Delta t }$

Where $\Delta \phi =$ magnetic flux = $\Delta BA$

Where $A =$ area of loop = $\pi r^{2}$

Average emf = $- \frac{0.021 \times \pi \times 16 \times 10^{-4} }{0.46}$

Magnitude of average emf = $2.29 \times 10^{-4} = 0.229$ mV

Thus, the magnitude of average induced emf = 0.229 mV