A flat loop of wire consisting of a single turn of cross-sectional area 7.30 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to 2.00 T in 0.93 s. What is the resulting induced current if the loop has a resistance of 1.30 ?

Respuesta :

As per Faraday's law of induction the EMF induced in the loop  is due to rate of change in magnetic flux linked with the loop

So here we can say

[tex]EMF = \frac{d\phi}{dt}[/tex]

[tex]EMF = A\frac{dB}{dt}[/tex]

[tex]EMF = A\frac{B_1 - B_2}{\Delta t}[/tex]

Given that

[tex]B_1 = 0.500 T[/tex]

[tex]B_2 = 0.200 T[/tex]

[tex]\Delta t = 0.93 s[/tex]

[tex]A = 7.30 cm^2[/tex]

now plug in all values in it

[tex]EMF = 7.30\times 10^{-4} (\frac{0.500 - 0.200}{0.93})[/tex]

[tex]EMF = 2.35 \times 10^{-4} Volts[/tex]

now in order to find induced current we can use Ohm's law

[tex]V = iR[/tex]

[tex]2.35 \times 10^{-4} = i (1.30)[/tex]

[tex]i = 1.81 \times 10^{-4} A[/tex]