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

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

     $B = \frac{\mu_o * N * I }{L}$

From this equation we see that

     $B \ \alpha \ \frac{N}{L}$

     $B = C \frac{N}{L}$

Here C stands for constant

=>   $C = \frac{B * \frac{L}{N}$

=>    $\frac{B_1 * \frac{L_1}{N_1} = \frac{B_2 * \frac{L_2}{N_2}$

=>  $\frac{B_1}{B_2 } = \frac{N_1 L _2}{ N_2L_1}$

=>   $\frac{B_1}{B_2 } = \frac{N_1 * (2 L_1)}{ (2 N_2)L_1}$

=>   $\frac{B_1}{B_2 } = 1$

=>   $B_2 = B_1$