Free MCAT study guide — Chemical and Physical Foundations of Biological Systems
Electricity and magnetism is a core MCAT physics topic covering electrostatics (Coulomb's law, electric fields and potentials, capacitors), circuits (Ohm's law, resistors in series and parallel, Kirchhoff's laws, power), and basic magnetism (magnetic fields, force on charges and current-carrying wires). You need to understand the relationships between charge, electric field, electric potential, and potential energy. Circuit analysis requires calculating equivalent resistance, current distribution, and voltage drops in series and parallel networks. Capacitors store charge and energy in electric fields and are tested both as isolated components and in circuits. The MCAT connects these concepts to biology through nerve impulse propagation (membrane as a capacitor, ion channels as variable resistors), cardiac defibrillators (capacitor discharge), and electrochemistry. Magnetic force on moving charges (F = qvBsin theta) and on current-carrying wires (F = BILsin theta) complete the topic, with applications to mass spectrometers, cyclotrons, and MRI technology.
Coulomb's law describes the electrostatic force between two point charges: F = kq1q2/r^2, where k = 8.99 x 10^9 N m^2/C^2 (approximately 9 x 10^9). The force is attractive between opposite charges and repulsive between like charges. The electric field is the force per unit positive test charge: E = F/q = kQ/r^2, directed away from positive charges and toward negative charges. Electric field lines start on positive charges and end on negative charges; they never cross. The field is stronger where lines are denser. For a uniform field between parallel plates: E = V/d (voltage divided by plate separation). A charge in an electric field experiences a force F = qE. The field inside a conductor at electrostatic equilibrium is zero (charges redistribute to cancel internal fields), and excess charge resides on the surface. Gauss's law provides an alternative way to calculate electric fields for symmetric charge distributions: the electric flux through a closed surface is proportional to the enclosed charge.
Electric potential (voltage) is the electric potential energy per unit charge: V = kQ/r for a point charge. Potential is a scalar quantity (no direction), unlike the electric field (vector). The potential due to multiple charges is the algebraic sum of individual potentials. Electric potential energy between two charges is U = kq1q2/r. A positive charge moves spontaneously from high potential to low potential (like a ball rolling downhill); a negative charge moves from low to high potential. The relationship between field and potential: E = -dV/dx, or for a uniform field, E = V/d. Equipotential surfaces are perpendicular to electric field lines and represent locations of equal potential. No work is done moving a charge along an equipotential surface. The work done by the electric field in moving charge q through a potential difference is W = qDeltaV. This concept connects to electrochemistry (cell potential), membrane potential in neurons (approximately -70 mV), and the electron volt (1 eV = 1.6 x 10^-19 J, the energy gained by an electron through a 1 V potential difference).
A capacitor stores charge on two parallel plates separated by a dielectric. Capacitance C = Q/V = epsilon_0 A/d for parallel plates (epsilon_0 = 8.85 x 10^-12 F/m). Capacitance increases with larger plate area, smaller separation, and higher dielectric constant (kappa): C = kappa x epsilon_0 x A/d. Energy stored: U = 1/2 CV^2 = 1/2 Q^2/C = 1/2 QV. In series: 1/C_total = 1/C1 + 1/C2 (total capacitance decreases, voltage divides). In parallel: C_total = C1 + C2 (total capacitance increases, voltage is the same across each). Note that capacitors combine OPPOSITE to resistors: series decreases capacitance, parallel increases it. A dielectric material between the plates increases capacitance, decreases electric field, and increases breakdown voltage. The cell membrane acts as a capacitor: the lipid bilayer is the dielectric (low dielectric constant, approximately 2), with charged solutions (cytoplasm and extracellular fluid) as the plates. The membrane potential (approximately -70 mV) represents charge separation across this biological capacitor.
Ohm's law: V = IR, where V is voltage (potential difference), I is current (charge flow rate, in amperes = coulombs/second), and R is resistance (in ohms). Resistance depends on material and geometry: R = rho L/A, where rho is resistivity, L is length, and A is cross-sectional area. Longer wires have more resistance; thicker wires have less. Resistors in series: R_total = R1 + R2 + ... (current is the same through each, voltages add). Resistors in parallel: 1/R_total = 1/R1 + 1/R2 + ... (voltage is the same across each, currents add). For two resistors in parallel: R_total = R1R2/(R1+R2). Kirchhoff's junction rule (conservation of charge): current in = current out at any junction. Kirchhoff's loop rule (conservation of energy): the sum of voltage changes around any closed loop = 0. Power dissipated: P = IV = I^2R = V^2/R. In a series circuit, the largest resistor dissipates the most power (P = I^2R, same I). In a parallel circuit, the smallest resistor dissipates the most power (P = V^2/R, same V).
Moving charges create magnetic fields and experience forces in external magnetic fields. The force on a moving charge in a magnetic field is F = qvBsin(theta), where theta is the angle between v and B. This force is perpendicular to both v and B (right-hand rule), so it does no work and only changes the direction of motion, not speed. A charge moving perpendicular to B follows a circular path with radius r = mv/(qB). This is the principle behind mass spectrometers (separating ions by mass-to-charge ratio) and cyclotrons (accelerating particles). The force on a current-carrying wire in a magnetic field is F = BILsin(theta), where L is the wire length. This is the principle behind electric motors. A current-carrying wire creates a magnetic field: for a long straight wire, B = mu_0 I/(2 pi r), where mu_0 = 4 pi x 10^-7 T m/A. The right-hand rule determines the field direction: thumb points in the direction of current, fingers curl in the direction of the magnetic field. Parallel currents in the same direction attract; opposite currents repel.
Faraday's law of induction states that a changing magnetic flux through a loop induces an electromotive force (EMF): EMF = -d(phi_B)/dt, where phi_B = BAcos(theta) is the magnetic flux. The magnitude of the induced EMF increases with the rate of change of flux. Lenz's law (the negative sign) states that the induced current flows in a direction that opposes the change in flux that produced it (conservation of energy). EMF can be induced by changing B, changing A, changing the angle theta, or any combination. This is the principle behind electric generators (rotating a coil in a magnetic field produces AC current), transformers (changing current in the primary coil induces EMF in the secondary coil: V_s/V_p = N_s/N_p), and electromagnetic braking. Applications in medicine include MRI (nuclear magnetic resonance), which uses strong magnetic fields and radiofrequency pulses to create detailed images of soft tissues, and transcranial magnetic stimulation (TMS), which uses changing magnetic fields to induce currents in brain tissue.
Coulomb's law: F = kq1q2/r^2. Like charges repel, opposite charges attract.
Electric field: E = kQ/r^2 (point charge) or E = V/d (parallel plates).
Electric potential: V = kQ/r (scalar). Potential energy: U = kq1q2/r.
Ohm's law: V = IR. Power: P = IV = I^2R = V^2/R.
Series resistors: R adds, same current, voltage divides. Parallel resistors: 1/R adds, same voltage, current divides.
Capacitance: C = Q/V. Series: 1/C adds. Parallel: C adds. (Opposite of resistors.)
Energy in a capacitor: U = 1/2 CV^2.
Magnetic force on a charge: F = qvBsin(theta). Perpendicular to both v and B, does no work.
Circular motion in a B field: r = mv/(qB). Basis for mass spectrometry.
Faraday's law: changing magnetic flux induces EMF. Lenz's law: induced current opposes the change.
1 electron volt (eV) = 1.6 x 10^-19 J.
The cell membrane acts as a capacitor with a resting potential of approximately -70 mV.
Kirchhoff's laws: junction rule (current conservation) and loop rule (energy conservation).
Confusing electric field (vector) with electric potential (scalar) -- field has direction, potential does not.
Forgetting that magnetic force does no work because it is always perpendicular to velocity -- it changes direction, not speed.
Mixing up series and parallel rules for capacitors vs. resistors -- they are OPPOSITE (series capacitors add reciprocally, series resistors add directly).
Using the wrong power formula: in series, use P = I^2R (same current); in parallel, use P = V^2/R (same voltage).
Forgetting that electric field inside a conductor is zero at equilibrium.
Confusing EMF (energy source, like a battery) with terminal voltage (EMF minus internal resistance drop: V = EMF - Ir).
Applying the right-hand rule incorrectly for negative charges -- the force on a negative charge is opposite to what the right-hand rule gives.
Practice circuit analysis systematically: (1) identify series and parallel groupings, (2) calculate equivalent resistance, (3) find total current from V = IR, (4) distribute current at junctions, (5) calculate voltage drops across each resistor, and (6) verify with Kirchhoff's loop rule. Start with simple circuits and build to complex networks. The MCAT often adds a twist, such as including a capacitor, an internal resistance in the battery, or asking about power dissipation.
For electrostatics and magnetism, practice drawing field lines, calculating forces, and predicting the motion of charges in electric and magnetic fields. Understand the connection between circular motion in a magnetic field and mass spectrometry (the MCAT loves this application). For electromagnetic induction, practice Faraday's law calculations and always check your answer with Lenz's law to ensure the direction makes physical sense. These topics integrate well with biology -- understand how neurons use electrochemical gradients and how medical imaging technologies rely on electromagnetic principles.
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