A solenoid is wound with 970 turns on a form 4.0 cm in diameter and 50 cm long.The windings carry a current I in the sense that is shown in the figure.The current produces a magnetic field,of magnitude near the center of the solenoid.Find the current in the solenoid windings.
A)1.8 A
B)1.5 A
C)1.3 A
D)2.2 A
E)2.0 A

Question

A solenoid is wound with 970 turns on a form 4.0 cm in diameter and 50 cm long.The windings carry a current I in the sense that is shown in the figure.The current produces a magnetic field,of magnitude  near the center of the solenoid.Find the current in the solenoid windings.  
A)1.8 A 
B)1.5 A 
C)1.3 A 
D)2.2 A 
E)2.0 A

Quizplus · Accepted Answer

We can use the expression for the magnetic field inside a solenoid:

B = μ0 * n * I

where B is the magnetic field, μ0 is the magnetic constant (4π × 10-7 T·m/A), n is the number of turns per unit length (n = N/L), and I is the current in the windings.

We can solve for I:

I = B / (μ0 * n)

The number of turns per unit length is:

n = N/L = (970 turns) / (0.5 m) = 1940 turns/m

Substituting the given values, we get:

I = (11eab929_2944_2220_99e6_1745444d2d10_TB4470_11 T) / (4π × 10-7 T·m/A * 1940 turns/m)

I ≈ 1.8 A

Therefore, the current in the solenoid windings is 1.8 A.

A Solenoid Is Wound with 970 Turns on a Form