A long wire carries a current of 20 A along the directed axis of a long solenoid. The field due to the solenoid is 4 mT. Find the field at a point 3 mm from the solenoid axis.
To find the magnetic field at a point 3 mm from the axis of the solenoid, we can use Ampere's Law. Ampere's Law states that the integral of the magnetic field along a closed loop is equal to the product of the current passing through the loop and the permeability of free space.
The magnetic field inside a solenoid is uniform and can be calculated using the formula:
B = μ₀ * n * I
Where:
B is the magnetic field,
μ₀ is the permeability of free space,
n is the number of turns per unit length (also known as the winding density),
I is the current passing through the solenoid.
In the given problem, the field due to the solenoid is 4 mT (millitesla), and the current passing through the solenoid is 20 A.
First, we need to convert the field from millitesla to tesla:
1 T = 1,000 mT
Therefore, 4 mT = 0.004 T
Next, we need to find the winding density, n. The winding density represents the number of turns per unit length. This information is not provided in the problem statement. So, to find the winding density, we need additional information.
Once we have the winding density, we can calculate the magnetic field at a point 3 mm from the solenoid axis using the formula mentioned above.