Answer:
The rate of change of magnetic field is 2.23 T/s.
Explanation:
Given that,
Dimension of rectangular coil is 7.2 cm by 3.7 cm.
Number of turns in the coil, N = 104
Resistance of the coil, R = 12.4 ohms
Current, I = 0.05 A
We need to find the rate of change of magnetic field in the coil. The induced emf is given by the rate of change of magnetic flux. So,
[tex]\epsilon=-\dfrac{d\phi}{dt}[/tex]
Ohm's law is :
[tex]\epsilon=IR[/tex]
So,
[tex]IR=-\dfrac{d\phi}{dt}\\\\IR=-\dfrac{d(NBA)}{dt}\\\\IR=-NA\dfrac{dB}{dt}\\\\\dfrac{dB}{dt}=\dfrac{IR}{NA}\\\\\dfrac{dB}{dt}=\dfrac{0.05\times 12.4}{104\times 7.2\times 10^{-2}\times 3.7\times 10^{-2}}\\\\\dfrac{dB}{dt}=2.23\ T/s[/tex]
So, the rate of change of magnetic field is 2.23 T/s.
