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elena55
1 month ago
14

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?

Physics
1 answer:
Sav [3.1K]1 month ago
4 0

Complete Question

The entire question is displayed in the first uploaded image

Answer:

The right choice is option  3

Explanation:

The question informs us 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

Typically, the magnetic field in a solenoid can be expressed mathematically as

     B = \frac{\mu_o * N * I }{L}

According to this formula we find that

     B \ \alpha \ \frac{N}{L}

     B = C \frac{N}{L}

Here C denotes 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

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