A long solenoid that has 990 turns uniformly distributed over a length of 0.410 m produces a magnetic field of magnitude 1.00 multiply.gif 10-4T at its center. What current is required in the windings for that to occur?
To find the current required in the windings of the solenoid, you can use the formula for the magnetic field inside a long solenoid:
B = μ₀ * n * I
Where:
B is the magnetic field (1.00 * 10^-4T)
μ₀ is the permeability of free space (4π * 10^-7 T*m/A)
n is the number of turns per unit length (990 turns/0.410 m)
I is the current in the windings (unknown)
Let's solve for I:
Rearranging the formula, we have:
I = B / (μ₀ * n)
Substituting the given values:
I = (1.00 * 10^-4T) / (4π * 10^-7 T*m/A * (990 turns / 0.410 m))
Now, let's calculate this value.
To determine the current required in the windings of the solenoid, we can use the formula for the magnetic field inside a long solenoid:
B = μ₀ * n * I
Where:
B is the magnetic field magnitude,
μ₀ is the permeability of free space (4π * 10^-7 T*m/A),
n is the number of turns per unit length (turns/m),
I is the current in the windings.
In this case, we are given:
B = 1.00 x 10^-4 T
n = 990 turns / 0.410 m
To find the current I, we rearrange the formula:
I = B / (μ₀ * n)
Substituting the given values:
I = (1.00 x 10^-4 T) / (4π x 10^-7 Tm/A * (990 turns / 0.410 m))
Simplifying the expression:
I = (1.00 x 10^-4) / (4π x 10^-7 * 990 / 0.41) A
Calculating the result:
I ≈ 7.69 A
Therefore, the current required in the windings of the solenoid is approximately 7.69 Amperes.