Chapter 20, Problem 21Q

To determine

(a) To determine:

The effect on B inside a long solenoid if the diameter of all the loops was doubled.

Answer to Problem 21Q

Solution:

The magnetic field inside the solenoid remains same if the diameter of all the loops is doubled.

Explanation of Solution

The magnetic field inside the solenoid is given by the equation $B=\frac{{\mu }_{o}NI}{l}$ where, N is the number of turns in the solenoid, l is the length of the solenoid and I is the current passing through the solenoid.

The magnetic field inside the solenoid is independent of the diameter of the solenoid. So, if diameter is doubled, the magnetic field inside the solenoid remains same.

To determine

(b) To determine:

The effect on B inside a long solenoid if the spacing between loops was doubled.

Answer to Problem 21Q

Solution:

The magnetic field inside the solenoid reduces by half if the spacing between loops is doubled.

Explanation of Solution

The magnetic field inside the solenoid is inversely proportional to length. If the spacing between loops was doubled, the length of the solenoid is doubled. Hence, magnetic field inside the solenoid reduces by half of the previous value.

To determine

(c) To determine:

The effect on B inside a long solenoid if the solenoid’s length was doubled along with a doubling in the total number of loops?

Answer to Problem 21Q

Solution:

The magnetic field inside the solenoid remains same if the solenoid’s length was doubled along with a doubling in the total number of loops.

Explanation of Solution

The magnetic field inside the solenoid is directly proportional to number of turns and inversely proportional to length. If the solenoid’s length was doubled along with a doubling in the total number of loops, the ratio of N to l remains same. Hence no change in the magnetic field.