A 5.0 amp current flows through a 0.20m long solenoid with 1500 loops
What are the magnitude and direction of the magnetic field at the centre of the solenoid?
To determine the magnitude and direction of the magnetic field at the center of a solenoid, you can use the formula for the magnetic field inside a solenoid, given by:
B = μ₀ * N * I
Where:
B is the magnetic field strength,
μ₀ is the permeability of free space (constant value),
N is the number of turns (loops) in the solenoid, and
I is the current flowing through the solenoid.
Given that the current I = 5.0 A, the length of the solenoid L = 0.20 m, and the number of turns N = 1500, we can calculate the magnetic field at the center of the solenoid.
First, let's determine the permeability of free space (μ₀):
μ₀ = 4π * 10^-7 T ⋅ m/A (tesla meter per ampere)
Next, substitute the values into the formula:
B = (4π * 10^-7 T ⋅ m/A) * 1500 * 5.0 A
Simplifying the calculation:
B = 3.7699 x 10^-2 T
The magnitude of the magnetic field at the center of the solenoid is approximately 3.7699 x 10^-2 Tesla.
Regarding the direction, the magnetic field inside a solenoid is uniform and parallel to the axis of the solenoid. Therefore, at the center of the solenoid, the magnetic field will be directed along its axis, perpendicular to the loops.
In summary, the magnitude of the magnetic field at the center of the solenoid is approximately 3.7699 x 10^-2 Tesla, and the direction is along the axis, perpendicular to the loops.