Quick Revision of Electric Potential and Capacitance

What is Electric Potential?

• Infinity: The point where the electric force is zero.
• Electric Potential: The work done in bringing a test charge from infinity to a point.
• Example:
  • Bringing 1 coulomb charge with 10 joules of work gives potential of 10 volts.
  • With 20 joules of work gives 20 volts.
• Potential Difference: Work done in moving a charge between two points.

Electric Field and Potential

• Potential decreases in the direction of the electric field.
• Potential increases against the direction of the electric field.
• 1 Volt: Bringing 1 coulomb charge with 1 joule of work.

Potential Difference

• Determines the direction of charge flow.
• Positive charge moves from higher to lower potential.
• Negative charge moves from lower to higher potential.

Electric Potential Due to a Point Charge

• To find the potential of charge q at point O.
• Formula: ( v = \frac{kq}{r} )

Electric Field vs Potential

• Potential: ( k \frac{q}{r} )
• Electric Field: ( k \frac{q}{r^2} )
• Electric field decreases more rapidly with distance.

Inside a Conducting Sphere

• Electric Field: Zero
• Potential: Constant and Maximum

Expression for Electric Potential

• Axial Point: Potential ( kp \frac{1}{r^2} )
• Equatorial Point: Potential is zero

Relation Between Electric Field and Potential

• Formula: ( e = - \frac{dv}{dx} )

Equipotential Surface

• All points have the same potential.
• Work done in moving charge is zero.
• Surfaces are closer in a strong electric field.

Electric Potential Energy

• System of Charges: ( U = k \frac{q1q2}{r} )
• Three Particle System: Detailed formula
• Negative Product: Negative potential energy
• Positive Product: Positive potential energy

Capacitor

• Capacitance: Ability to store charge.
• Formula: ( C = \frac{Q}{V} )
• Capacitance of a Capacitor: Does not depend on charge.

Capacitance of Parallel Plate Capacitor

• Formula: ( C = \varepsilon_0 \frac{A}{d} )
• Dielectric Slab: Increases capacitance.

Combination of Capacitors

• Series: ( \frac{1}{C} = \frac{1}{C1} + \frac{1}{C2} + \frac{1}{C3} )
• Parallel: ( C = C1 + C2 + C3 )