Question

Font Paragraph Dyes Q4) (8 Points) A long solenoid with 100 turns has a radius of 0.Im and its length is 0.8m. The curent through the solenoid increases according to the relation l(t)-6t+St. A) Calculate the self-inductance voltage in the solenoid at t-2s. B) What is the induced current if its resistance is 52 C What is the direetion of both induced magnetic field and current in the solenoid 1000000000000001

Answer 1

a) Length of solenoid, L = 0.8 m
radius, r =0.1 m
I(t) = 6t^3+5t
Self inductance of a solenoid, L = u0 N^2 pi r^2/ l = 4π*10^-7*100^2*π*0.1*0.1/0.8 = 0.00049348 H
Induced emf(self inductance voltage), e = -Ldi/dt = -0.00049348*(18t^2+5)
At t = 2s, e = -0.038 Volt
b) Induced current, i = e/R = 0.038/5 = -0.0076 A
c) Opposite to the direction of the current through the solenoid.
The current through the solenoid in the figure is clockwise as seen from right into the solenoid, the direction of induced current will be counterclockwise as seen from left.
Use right hand thumb rule to get the direction of the magnetic field.