Question

A coil 3.60 cm radius, containing 600 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10−2 T/s )t+( 3.35×10−5 T/s4 )t4. The coil is connected to a 660-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.Find the magnitude of the induced emf in the coil as a function of time.

Answer 1

Answer:

the emf will be $2.4(1.20\times 10^{-2}+13.4\times 10^{-5}t^3)$

Explanation:

We have given radius of the coil r = 3.6 cm = 0.036 m

So area $A=\pi r^2=3.14\times 0.036^2=0.0040m^2$

Number of turns N = 600

Emf is given by $e=N\frac{d\Phi }{dt}$

$e=N\frac{d\Phi }{dt}=NA\frac{dB}{dt}=600\times 0.0040\times d\frac{1.20\times 10^{-2}t+3.35\times 10^{-5}t^4}{dt}=2.4(1.20\times 10^{-2}+13.4\times 10^{-5}t^3)$

So the emf will be $2.4(1.20\times 10^{-2}+13.4\times 10^{-5}t^3)$