Question

Solenoid №1 has a length L, cross-sectional area A, and N turns. Solenoid №2 has a length 2 L, cross-sectional area 2 A, and 2 N turns. Which solenoid has the greater magnetic field at its center when equal currents are going through them?

Answer 1

Answer:

Both solenoid have same magnetic field.

Explanation:

We are given that

Number of turns of  solenoid$N_{01}=N$

Cross sectional area of  solenoid$N_{01}=A$

Length of solenoid$N_{01}=L$

Number of turns of solenoid$N_{02}=2N$

Cross sectional area of  solenoid$N_{02}=2A$

Length of solenoid$N_{02}=2L$

Let current flowing in each solenoid=I

Magnetic field of solenoid=$\frac{\mu_0IN}{L}$

Magnetic field of  solenoid$N_{01}=\frac{\mu_0NI}{L}$

Magnetic field of  solenoid$N_{02}=\frac{\mu_0I(2N)}{2L}=\frac{\mu_0IN}{L}$

Hence, both solenoid have same magnetic field.