\[B=\frac{\mu_0NI}{L}\]
Variables
Bmagnetic field strength inside the solenoid (T)
mu0vacuum permeability (H/m)
Nnumber of turns
Ielectric current (A)
Lsolenoid length (m)
Description
What is this formula?
This formula calculates the magnetic field inside a long solenoid. For an ideal solenoid, the magnetic field is approximately uniform inside and depends on the current, number of turns, and solenoid length.
When to use it
Use this formula when analyzing coils, electromagnets, inductors, laboratory solenoids, and magnetic field generation systems.
Example
A solenoid has 800 turns, a length of 0.5 m, and carries a current of 2 A. Calculate the magnetic field inside the solenoid.
Data:
N = 800
I = 2 A
L = 0.5 m
mu0 = 4*pi*10^-7 H/m
Formula:
B = (mu0*N*I)/L
Substitution:
B = ((4*pi*10^-7)*800*2)/0.5
Result:
B = 4.02 × 10^-3 T
Applications
- Electromagnet design
- Solenoid actuators
- Magnetic field generation
- Inductor analysis
- Physics laboratory experiments