Electrostatic Potential and Capacitance
Class 12 · Physics
4 ideas in Class 12 Physics, explained in plain words, with games and quizzes to practise.
Electrostatic Potential and Equipotentials
Part of: Potential and Equipotentials
Potential at a point is the work needed to bring a unit positive charge there from infinity, divided by that charge. Surfaces joining points of equal potential are called equipotentials: no work is done moving along them, and field lines always cut them at right angles.
Why it matters. Circuits, batteries and capacitors are all described with potential, not force. Forgetting that potential adds as a number while field adds as arrows is the most common source of sign errors.
Formulas
- Potential from work: V = W / q
- Point charge: V = k Q / r, zero at infinity
- Field from potential: E points from high V to low V
Key words
- Electrostatic potential
- : Work per unit positive charge to reach a point from infinity, measured in volts.
- Volt
- : One joule of work per coulomb of charge moved between two points.
- Equipotential surface
- : A surface where every point is at the same potential, so no work is done along it.
- Potential difference
- : Work per unit charge to move between two points, equal to V2 minus V1.
Try it in two minutes
- Divide the work done on a charge by the charge to get the potential change.
- Sketch circles around a point charge as its equipotentials.
- Draw field arrows leaving the circles at right angles.
Try at home. Explain why a bird sitting on one high-voltage wire feels nothing.
Potential Energy and Dipole in a Field
Part of: Potential and Equipotentials
The potential energy of two charges is the work needed to assemble them from infinity, positive for like charges and negative for opposite ones. A dipole in an external field has lowest energy when aligned with the field and feels a torque otherwise, turning it toward alignment.
Why it matters. Energy signs tell whether charges are bound or free, and dipole alignment explains polar molecules and antennas. Sign slips here reverse every conclusion about stability.
Formulas
- Pair energy: U = k q1 q2 / r
- System energy: add U for every pair once
- Dipole in field: U = -p E cos(theta)
Key words
- Potential energy
- : Work stored while assembling charges from infinity, recoverable when they move apart.
- Bound system
- : A charge pair with negative total energy that needs outside work to separate.
- Dipole alignment
- : The lowest-energy state of a dipole, pointing along the external field.
Try it in two minutes
- Multiply the two charges, divide by their gap, and multiply by k.
- Keep the sign: opposite charges give negative stored energy.
- For a dipole, note the angle with the field and use minus pE cos of it.
Try at home. Predict whether bringing a third charge near a pair raises or lowers the total energy, then check with numbers.
Conductors, Dielectrics and Capacitors
Part of: Conductors, Dielectrics and Capacitors
Inside a conductor in balance the field is zero and excess charge sits on the surface. A dielectric is an insulator whose molecules stretch or turn in a field, weakening it. A capacitor stores charge on two plates, with capacitance defined as charge per volt and raised by a dielectric slab.
Why it matters. Shielding, insulators in cables and every capacitor depend on these ideas. Believing charge stays inside a conductor's volume, or that any insulator behaves the same in a field, breaks circuit predictions.
Formulas
- Capacitance: C = Q / V
- Parallel plate: C = e0 A / d
- With dielectric: C = K e0 A / d
Key words
- Electrostatic shielding
- : Protection of an inner region by a conductor, inside which the field stays zero.
- Dielectric
- : An insulating material that weakens an applied field by molecular alignment.
- Capacitance
- : Charge stored per volt on a capacitor, measured in farads.
- Dielectric constant
- : The factor by which a material raises capacitance compared with empty space.
Try it in two minutes
- Argue why free charges in a conductor must cancel any inside field.
- Compare a polar molecule with a stretched non-polar one.
- Show that wider plates or a smaller gap raise capacitance.
Try at home. Slide a plastic sheet between two charged plates in thought and predict the voltage change.
Capacitor Networks and Stored Energy
Part of: Capacitor Networks and Stored Energy
Capacitors in series share the same charge with voltage split across them, giving a smaller equivalent. In parallel each feels the full voltage and charges add, giving a larger equivalent. A charged capacitor stores energy equal to half QV, which grows with the square of the voltage.
Why it matters. Real circuits use banks of capacitors for filtering, timing and smoothing. Adding series capacitors like resistors, or missing the square in the energy, gives wrong voltages and energies.
Formulas
- Series: 1/C = 1/C1 + 1/C2
- Parallel: C = C1 + C2
- Stored energy: U = QV/2 = CV^2/2 = Q^2/(2C)
Key words
- Series combination
- : Capacitors joined end to end, all carrying the same charge with split voltage.
- Parallel combination
- : Capacitors joined side by side, all sharing the same voltage with added charge.
- Equivalent capacitance
- : The single capacitance that behaves like a whole network between two terminals.
Try it in two minutes
- For series, invert each value, add, and invert back.
- For parallel, simply add the values.
- Multiply half the charge by the voltage for the stored energy.
Try at home. Predict which stores more energy at 10 V: 6 and 3 units in series or in parallel.
What your child will practise
- Capacitor Networks and Stored Energy: Jungle Quick Fire (Quick Fire)
- Conductors, Dielectrics and Capacitors: Candy Quick Fire (Quick Fire)
- Conductors, Dielectrics and Capacitors: Space Puzzle (Clue Puzzle)
- Electrostatic Potential and Equipotentials: Desert Quick Fire (Quick Fire)
- Potential Energy and Dipole in a Field: Jungle Puzzle (Clue Puzzle)
- Quiz: Capacitor Networks and Stored Energy (8 questions)
- Quiz: Conductors, Dielectrics and Capacitors (8 questions)
- Quiz: Electrostatic Potential and Equipotentials (8 questions)
- Quiz: Potential Energy and Dipole in a Field (8 questions)