A long solenoid that has 1200 turns uniformly distributed over a length of 0.37 m is required to produce a magnetic field of magnitude 0.02mT at its center. what voltage should be applied across the solenoid if it has a resistance of 20ohms?
can someone give me the equation of this concept and tell me what concept it is?
The concept involved here is the relationship between magnetic field, current, and length of a solenoid. The equation that represents this concept is given by Ampere's Law:
B = μ0 * n * I
Where:
B is the magnetic field strength
μ0 is the magnetic constant (4π x 10^-7 T·m/A)
n is the number of turns per unit length (turns/m)
I is the current flowing through the solenoid (A)
To solve for the voltage that needs to be applied across the solenoid, we need to determine the current flowing through it.
The resistance of the solenoid is given as 20 ohms, which means the current can be calculated using Ohm's Law:
I = V / R
Where:
I is the current (A)
V is the voltage (V)
R is the resistance (ohms)
Now let's substitute the equation for current into Ampere's Law and solve for the voltage:
B = μ0 * n * (V / R)
Rearranging the equation to solve for V:
V = (B * R) / (μ0 * n)
Given values:
B = 0.02 mT = 0.02 × 10^-3 T
n = 1200 turns / 0.37 m
R = 20 ohms
μ0 = 4π × 10^-7 T·m/A
Plug in the values and solve for V:
V = (0.02 × 10^-3 T * 20 ohms) / (4π × 10^-7 T·m/A * (1200 / 0.37) turns/m)
Simplifying the equation will give you the voltage that needs to be applied across the solenoid.