Shortcut Methods
Electrostatics
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Electric field due to a point charge
- To find the electric field, use Coulomb’s law, which states that the electric field strength (E) at a point is directly proportional to the charge (q) of the point charge and inversely proportional to the square of the distance (r) from the charge.
- Shortcut method:
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Electric potential due to a point charge
- To find the electric potential, use the formula that the electric potential (V) at a point is directly proportional to the charge (q) of the point charge and inversely proportional to the distance (r) from the charge.
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Gauss’s law
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To apply Gauss’s law, calculate the surface integral of the electric field over a closed surface, and set it equal to the total charge (Q_{inside}) divided by the permittivity of free space (\epsilon_0).
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Shortcut method:
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Capacitance of a parallel-plate capacitor
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To find the capacitance, use the formula
where (\epsilon) is the permittivity of the material between the plates, (A) is the area of the plates, and (d) is the distance between the plates. -
Shortcut method: (C\propto \frac{A}{d})
Electromagnetics
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Ampère’s law
- To use Ampère’s law, calculate the line integral of the magnetic field around a closed loop, and set it equal to the total current (I_{enclosed}) flowing through the loop multiplied by the permeability of free space (\mu_0).
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Faraday’s law of induction
- To use Faraday’s law, calculate the line integral of the electric field around a closed loop, and set it equal to the negative rate of change of the magnetic flux (\Phi_B).
- Shortcut method
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Lenz’s law
- Remember that the direction of an induced current opposes the change in magnetic flux.
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Shortcut method: Induced current creates an opposing magnetic field
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Motor/Generator basics:
- Motor converts electrical to mechanical energy.
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Generator converts mechanical to electrical energy.