Question

Two solenoids stand side-by-side. Solenoid B differs from solenoid A in three respects. Its total current is 2 times as great, it has 4 times as many coils, and it is 3 times as long. How do the magnetic fields inside the two solenoids compare?
1. Solenoid B’s magnetic field is 24 times greater than solenoid A's magnetic field.
2. Solenoid A’s magnetic field is 24 times greater than solenoid B's magnetic field.
3. Solenoid B’s magnetic field is 6 times greater than solenoid A's magnetic field.
4. Solenoid A’s magnetic field is 2.7 times greater than solenoid B's magnetic field.
5. Solenoid B’s magnetic field is 2.7 times greater than solenoid A's magnetic field.

Answer 1

Answer:

5. Solenoid B’s magnetic field is 2.7 times greater than solenoid A's magnetic field.

Explanation:

The magnetic field produced by a solenoid depends on number of coils, the length of the solenoid and the amount of current flowing through the coil.

$B=\frac{\mu \times N \times I}{L}$

Current in solenoid B is 2 times greater than the current in solenoid A.

$I_B=2I_A$

Number of coils in B is 4 times greater than coils in A

$N_B=4N_A$

Length of the solenoid B is 3 times greater than solenoid A

$L_B=3L_A$

$B_B=\frac{2\times 4}{3} B_A=2.7 B_A$

Thus, solenoid B's magnetic field is 2.7 times greater than magnetic field of solenoid A.