Electromagnetism is the backbone of modern technology, from circuits to electromagnetic waves. With Moogle Math’s Electromagnetism Solver, you can understand core concepts, solve complex problems, and explore real-world applications in physics and engineering.
1. Coulomb’s Law
Example: Calculate the force between two charges \( q_1 = 3 \, \mu C \) and \( q_2 = -2 \, \mu C \), separated by a distance \( r = 0.5 \, \text{m} \).
Input: force_between_charges(q1=3e-6, q2=-2e-6, distance=0.5)
2. Electric Field Strength
Example: Find the electric field at a point \( r = 0.2 \, \text{m} \) away from a charge \( q = 5 \, \mu C \).
Input: electric_field(charge=5e-6, distance=0.2)
3. Gauss’s Law
Example: Determine the electric flux through a spherical surface of radius \( r = 0.3 \, \text{m} \) enclosing a charge \( Q = 2 \, \mu C \).
Input: electric_flux(charge=2e-6, radius=0.3)
4. Magnetic Force
Example: Calculate the force on a charge \( q = 1.5 \, \mu C \) moving with velocity \( v = 200 \, \text{m/s} \) in a magnetic field \( B = 0.5 \, \text{T} \).
Input: magnetic_force(charge=1.5e-6, velocity=200, magnetic_field=0.5)
5. Faraday’s Law of Induction
Example: Find the induced EMF in a coil of \( N = 50 \) turns with a magnetic flux change \( \Delta \Phi = 0.1 \, \text{Wb} \) in \( \Delta t = 0.02 \, \text{s} \).
Input: induced_emf(turns=50, flux_change=0.1, time_change=0.02)
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Example: Determine the total resistance in a parallel circuit with \( R_1 = 4 \, \Omega \), \( R_2 = 6 \, \Omega \), and \( R_3 = 12 \, \Omega \).
Input: parallel_resistance(R1=4, R2=6, R3=12)
Input: wave_wavelength(frequency=3e8)
Example: Compute the capacitance of a capacitor with \( A = 0.01 \, \text{m}^2 \), \( d = 0.001 \, \text{m} \), and \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \).
Input: capacitance(area=0.01, distance=0.001, permittivity=8.85e-12)
Example: Find the magnetic field at a point \( r = 0.05 \, \text{m} \) from a long wire carrying current \( I = 10 \, \text{A} \).
Input: magnetic_field(current=10, distance=0.05)