Answered

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 :

lublana

Answer:

Both solenoid have same magnetic field.

Explanation:

We are given that

Number of turns of  solenoid[tex]N_{01}=N[/tex]

Cross sectional area of  solenoid[tex]N_{01}=A[/tex]

Length of solenoid[tex]N_{01}=L[/tex]

Number of turns of solenoid[tex]N_{02}=2N[/tex]

Cross sectional area of  solenoid[tex]N_{02}=2A[/tex]

Length of solenoid[tex]N_{02}=2L[/tex]

Let current flowing in each solenoid=I

Magnetic field of solenoid=[tex]\frac{\mu_0IN}{L}[/tex]

Magnetic field of  solenoid[tex]N_{01}=\frac{\mu_0NI}{L}[/tex]

Magnetic field of  solenoid[tex]N_{02}=\frac{\mu_0I(2N)}{2L}=\frac{\mu_0IN}{L}[/tex]

Hence, both solenoid have same magnetic field.

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