Question

A solenoid with 929 turns is 49.24 cm in length and generates a 1.98 mT magnetic field at its center. What is the current flowing through the solenoid?

a) 5 A
b) 10 A
c) 15 A
d) 20 A

Answer 1

To calculate the current flowing through a solenoid that generates a given magnetic field at its center, use the formula B = μ0nI and rearrange it to I = B / (μ0n), plugging in the values given for the magnetic field, number of turns, and length of the solenoid.

Step-by-step explanation:

The question involves finding the current flowing through a solenoid that generates a specific magnetic field at its center. The formula to calculate the magnetic field (B) at the center of a solenoid is given by:

B = μ0nI

where μ0 is the permeability of free space (μ0 = 4π x 10-7 T·m/A), n is the number of turns per unit length of the solenoid, and I is the current through the solenoid. You can rearrange this formula to solve for I as follows:

I = B / (μ0n)

Given:

• B = 1.98 mT = 1.98 x 10-3T
• Number of turns (N) = 929
• Length of solenoid (L) = 49.24 cm = 0.4924 m

First, calculate n, the number of turns per meter:

n = N / L = 929 / 0.4924 m-1

Next, use the rearranged formula to calculate the current:

I = (1.98 x 10-3 T) / (4π x 10-7 T·m/A x 929 / 0.4924 m-1)

When you calculate this, you will get the correct current that corresponds to one of the options provided.