Self-Induced EMF and Inductance Calculator

Formulas

The formulas to calculate the self-induced EMF and inductance are:

Self-Induced EMF:

\[ u_i = L \frac{\Delta I}{\Delta t} \]

Inductance:

\[ L = \frac{N^2 \mu_0 \mu_r A}{l} \]

Where:

\( u_i \) is the self-induced EMF in volts (V)
\( L \) is the inductance in henries (H)
\( N \) is the number of turns
\( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{H/m}\))
\( \mu_r \) is the relative permeability of the core material
\( A \) is the cross-sectional area in square meters (m²)
\( l \) is the length of the coil in meters (m)
\( \Delta I \) is the change in current in amperes (A)
\( \Delta t \) is the time change in seconds (s)

What is Self-Induced EMF and Inductance?

Self-induced EMF is the voltage generated in a coil due to a change in current through it, as described by Lenz's Law and Faraday's Law of Electromagnetic Induction. Inductance is a property of a coil that quantifies its ability to induce an EMF in itself when the current through it changes.

Example Calculation

Let's assume the following values:

Number of Turns (\( N \)): 100
Relative Permeability (\( \mu_r \)): 200
Cross-sectional Area (\( A \)): 0.01 m²
Length of the Coil (\( l \)): 0.5 m
Change in Current (\( \Delta I \)): 5 A
Time Change (\( \Delta t \)): 0.1 s

Step 1: Calculate the inductance:

\[ L = \frac{100^2 \times 4\pi \times 10^{-7} \times 200 \times 0.01}{0.5} \approx 0.502 \text{ H} \]

Step 2: Calculate the self-induced EMF:

\[ u_i = 0.502 \times \frac{5}{0.1} = 25.1 \text{ V} \]