A toroidal solenoid has 590 turns, cross-sectional area 6.20 cm^2 , and mean radius 5.00 cm .Part A. Calcualte the coil's self-inductance. Part B. If the current decreases uniformly from 5.00 A to 2.00 A in 3.00 ms, calculate the self-induced emf in the coil. Part C. The current is directed from terminal a of the coil to terminal b. Is the direction of the induced emf froma to b or from b to a?

Complete Question

A toroidal solenoid has 590 turns, cross-sectional area 6.20 cm^2 , and mean radius 5.00 cm .

Part A. Calculate  the coil's self-inductance.

Part B. If the current decreases uniformly from 5.00 A to 2.00 A in 3.00 ms, calculate the self-induced emf in the coil.

Part C. The current is directed from terminal a of the coil to terminal b. Is the direction of the induced emf from a to b or from b to a?

Part A  

Part B  

Part C

    From terminal a to terminal b

Explanation:

From the question we are told that

      The  number of turns is  

      The cross-sectional area is  

      The  radius is

Generally the coils self -inductance is mathematically represented as

Where is the permeability of  free space with value

substituting values

Considering the Part B

      Initial current is

      Current at time t is

       The  time taken is  

The self-induced emf is mathematically evaluated as

=>        

substituting values

The direction of the induced emf is  from a to b because according to Lenz's law the induced emf moves in the same direction as the current

the force required to move the cart is divided by three or 33.33 n.