Physics: Electricity, Circuits, and Magnetism

Electricity and magnetism questions on the MCAT Chem/Phys section reward conceptual reasoning over heavy computation. If you understand how charge creates fields, how fields drive current, how resistors combine, and how moving charges feel magnetic forces, you can reason through most items with a few standard formulas.

Core Idea

• Charges create electric fields; fields exert forces and store energy. Like charges repel, opposites attract, and the force follows Coulomb's law, which falls off as the inverse square of distance.
• Voltage drives current through resistance. Ohm's law, V = IR, ties the three together, and power delivered is P = IV.
• Moving charges feel magnetic forces, and changing magnetic flux induces voltage. This link between electricity and magnetism underlies motors, generators, and induction.

Electric Charge, Coulomb's Law, and Fields

Charge is quantized in units of the elementary charge (about 1.6 x 10^-19 C) and is conserved. Coulomb's law gives the force between two point charges: F = kq1q2 / r^2, where k is about 9 x 10^9 N.m^2/C^2. The force is attractive for opposite charges and repulsive for like charges, and it weakens with the square of the separation.

An electric field E is the force per unit charge, E = F/q, measured in N/C or V/m. Field lines point away from positive charges and toward negative charges. A positive test charge accelerates along the field; a negative charge accelerates opposite to it.

Electric Potential (Voltage) and Capacitors

Electric potential (voltage) is potential energy per unit charge, measured in volts. Positive charges move spontaneously from high to low potential, like a ball rolling downhill; negative charges move the opposite way. The relationship E = V/d applies for a uniform field between parallel plates.

A capacitor stores charge and energy in the electric field between two plates, with Q = CV. Capacitance C depends on plate area, separation, and any dielectric between the plates — not on the charge stored. Inserting a dielectric raises capacitance and lets the capacitor store more charge at a given voltage.

Current, Ohm's Law, Resistance, and Power

Current I is the rate of charge flow (charge per time), measured in amperes. Conventional current points in the direction positive charge would flow. Ohm's law, V = IR, states that voltage equals current times resistance.

Resistance opposes current and depends on the material and geometry: R = rho.L / A. A longer wire has more resistance; a thicker (larger cross-section) wire has less. Resistivity rho is an intrinsic property of the material. Electrical power dissipated is P = IV, which can be rewritten as P = I^2.R or P = V^2/R.

Series vs. Parallel Circuits

• Series: components share one path. Current is the same through each element. Resistances add: R_total = R1 + R2 + ..., so total resistance increases. Voltage divides across the resistors.
• Parallel: components share the same two nodes. Voltage is the same across each branch. Resistances add reciprocally: 1/R_total = 1/R1 + 1/R2 + ..., so total resistance is less than the smallest individual resistor. Current divides among the branches.
• Capacitors behave oppositely to resistors: capacitances add in parallel and combine reciprocally in series.

Magnetism and Electromagnetic Induction

A moving charge or a current creates a magnetic field, and a charge moving through a magnetic field feels a force F = qvB.sin(theta). The force is maximum when velocity is perpendicular to the field and zero when the charge moves parallel to it. The force is always perpendicular to both v and B (use the right-hand rule), so a magnetic field does no work and only changes direction, producing circular or helical motion.

Electromagnetic induction: a changing magnetic flux through a loop induces a voltage (EMF), the basis of Faraday's law. Lenz's law says the induced current opposes the change that created it. A static field induces nothing — only change matters.

High-Yield Exam Patterns

• Expect conceptual "what happens if" questions: double the distance in Coulomb's law and force drops to one-fourth (inverse square).
• Know that series adds resistance while parallel lowers it below the smallest resistor — a favorite trap.
• Use P = I^2.R vs P = V^2/R correctly: pick the form matching the quantity held constant.
• Magnetic force is zero when a charge moves parallel to the field and maximal when perpendicular.
• Remember a magnetic field does no work on a moving charge — it only redirects it.
• For induction, look for the word "changing"; a constant flux induces no current.

Common Traps to Avoid

• Treating Coulomb's law or field strength as linear with distance — both are inverse-square (field as 1/r^2, potential as 1/r).
• Assuming voltage is the same in series or current is the same in parallel — it is the reverse.
• Thinking capacitance depends on the charge stored; it depends only on geometry and dielectric.
• Forgetting that a magnetic field does no work and cannot change a charge's speed.
• Believing a steady magnetic field induces current — only a changing flux does.