A solenoid is made up of 100 turns of a wire carrying 0.25 A of current,and is 5.0 cm long.The radius of the solenoid is 1.5cm.You are looking at the solenoid end-on,such that the current circulates counter-clockwise from your point of view.A complete circuit is made by having the wire from one end of the solenoid connect to the wire at the other end,and running down the middle of the solenoid,therefore carrying current in the +z direction along the z-axis.What is the magnetic field at a point (x,y)= (-0.75 cm,0.0 cm)?
E)None are correct.

Question

Quizplus · Accepted Answer

Using the formula for the magnetic field inside a solenoid, 
B = μ₀nI,
where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. 
n = N/L = 100/0.05 = 2000 turns/meter 
B = (4π×10⁻⁷ T·m/A)·(2000 turns/m)·(0.25 A) = 0.628 T

Since the magnetic field is parallel to the z-axis, we can find the field at the given point by calculating the distance to the z-axis and multiplying by the field strength. 
The distance from the point (-0.75cm,0cm) to the z-axis is 0.75 cm. 
Therefore, 
B = (0.75 cm)(0.628 T) = 0.471 T

The magnetic field at the point is therefore 0.471 T in the -x direction.

A Solenoid Is Made Up of 100 Turns of a Wire