A solenoid with a nickel core has 1000 turns on 0.5 m. The cross-sectional area of
turn is 50 cm2. What is the magnetic field energy when a current 10 A passes
through it ? Given permeability of nickel is 200.
To calculate the magnetic field energy of a solenoid, we first need to find the magnetic field strength (B) using the formula:
B = (μ * N * I) / l
Where:
B is the magnetic field strength
μ is the permeability of nickel
N is the number of turns in the solenoid
I is the current passing through the solenoid
l is the length of the solenoid
Substituting the given values:
μ = 200
N = 1000
I = 10 A
l = 0.5 m
B = (200 * 1000 * 10) / 0.5
Next, we need to find the magnetic field energy (W) using the formula:
W = (1/2) * μ * I^2 * V
Where:
W is the magnetic field energy
μ is the permeability
I is the current passing through the solenoid
V is the volume of the solenoid
The volume (V) of the solenoid can be calculated using the formula:
V = A * l
Where:
A is the cross-sectional area of a turn
l is the length of the solenoid
Substituting the given values:
A = 50 cm^2 = 0.005 m^2
l = 0.5 m
V = 0.005 * 0.5
Finally, substituting the values into the formula for magnetic field energy:
W = (1/2) * 200 * (10^2) * (0.005 * 0.5)
Now you can calculate the magnetic field energy by simplifying the equation.