We need to find the current in the coil at t=2 seconds. Step 1: Find the induced EMF. The magnetic flux is given by φ=50t2+4. To find the EMF ( E ), we take the derivative of φ with respect to t : E=
dφ
dt
Now, differentiate φ :
d
dt
(50t2+4)=100t (because the derivative of t2 is 2t, and 50 times 2t is 100t; the derivative of a constant is 0 ). Step 2: Calculate EMF at t=2 seconds. Plug in t=2 : E=100×2=200 volts Step 3: Find the current using Ohm's Law. Ohm's Law: I=
E
R
Here, E=200 volts and R=200Ω. I=
200
200
=1A So, the current induced in the coil at t=2 seconds is 1 ampere.
