Electromagnetic Induction

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.