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

Both solenoid have same magnetic field.

Step-by-step 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=
`(\mu_0IN)/(L)`

Magnetic field of solenoid
`N_(01)=(\mu_0NI)/(L)`

Magnetic field of solenoid
`N_(02)=(\mu_0I(2N))/(2L)=(\mu_0IN)/(L)`

Hence, both solenoid have same magnetic field.