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 [tex]d_1[/tex]
The length of solenoid 1 is [tex] L_1 [/tex]
The number of turns of solenoid is [tex]N_1 [/tex]
The diameter of solenoid 2 is [tex]d_2 = 2d_1[/tex]
The length of solenoid 2 is [tex] L_2 = 2L_1 [/tex]
The number of turns of solenoid 2 is [tex] N_2 = 2 N_1 [/tex]
Generally the magnetic in a solenoid is mathematically represented as
[tex]B = \frac{\mu_o * N * I }{L}[/tex]
From this equation we see that
[tex]B \ \alpha \ \frac{N}{L}[/tex]
[tex]B = C \frac{N}{L}[/tex]
Here C stands for constant
=> [tex]C = \frac{B * \frac{L}{N}[/tex]
=> [tex]\frac{B_1 * \frac{L_1}{N_1} = \frac{B_2 * \frac{L_2}{N_2} [/tex]
=> [tex]\frac{B_1}{B_2 } = \frac{N_1 L _2}{ N_2L_1}[/tex]
=> [tex]\frac{B_1}{B_2 } = \frac{N_1 * (2 L_1)}{ (2 N_2)L_1}[/tex]
=> [tex]\frac{B_1}{B_2 } = 1[/tex]
=> [tex]B_2 = B_1[/tex]
