Question

Solenoid 2 has twice the diameter, twice the length, and twice as many turns as solenoid 1. How does the field B2 at the center of solenoid 2 compare to B1 at the center of solenoid 1?

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The correct option is option 3

Step-by-step explanation:

From the question we are told that

The diameter of solenoid 1 is
`d_1`

The length of solenoid 1 is
`L_1`

The number of turns of solenoid is
`N_1`

The diameter of solenoid 2 is
`d_2 = 2d_1`

The length of solenoid 2 is
`L_2 = 2L_1`

The number of turns of solenoid 2 is
`N_2 = 2 N_1`

Generally the magnetic in a solenoid is mathematically represented as

`B  =  (\mu_o *  N  *  I )/(L)`

From this equation we see that

`B  \ \alpha \  (N)/(L)`

`B   =  C   (N)/(L)`

Here C stands for constant

=>

=>

=>
`(B_1)/(B_2 )  =  (N_1 L _2)/( N_2L_1)`

=>
`(B_1)/(B_2 )  =  (N_1 * (2 L_1))/( (2 N_2)L_1)`

=>
`(B_1)/(B_2 )  =  1`

=>
`B_2 = B_1`