Chapter 2 Electrostatic Potential and Capacitance
- Two charges 5 x 10-8 C and – 3 x 10-8 C are located 16 cm apart. At what point(s) On the line there are two locations where potential becomes zero. For P, frac5 × 10⁻⁸x = frac3 × 10⁻⁸16-x 5( 16 - x) = 3x 80 - 5x = 3x 8x =... 1
- Two charges 2 μC and -2 μC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system (a) For the given system of the two charges, the equipotential surface will be a plane normal to the line AB joining the two charges and pas... 1
- The spherical conductor of radius 12 cm has a charge of 1.6 x 10-7 C distributed uniformly on its surface. R = 12 x 10⁻² m, Q = 1.6 x 10⁻⁷C (a) Zero (b) E = frac9 × 10⁹ × 1.6 × 10⁻⁷(12 × 10⁻²)² = frac9 × 10⁹ × 1.6 × 10⁻⁷12 × 12 × 10⁻⁴ = 10⁵ NC⁻¹ (... 1
- A parallel plate capacitor with air between the plates has a capacitance of 8 pF (lpF = 10-12F). C = 8pF, C = fracε₀ ~A~d C' = fracε_r ε₀ ~Ad/2 = 2ε_r ∴ C' = 2 x 6 x 8 x 10⁻¹² F = 96 pF 1
- In a parallel plate capacitor with air between the plates, each plate has an area of 6 x 10-3 m2 A = 6 x 10⁻³ m² d = 3 mm = 3 x 10⁻³m C = fracε₀ ~A~d = frac8.85 × 10⁻¹² × 6 × 10⁻³3 × 10⁻³ = 17.70 x 10⁻¹² = 17.7 pF Q = CV = 17.7 x 10⁻¹² x... 1
- A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor? C = 12 pF, V = 50V E = 1 / 2 CV² = 1 / 2 x 10⁻¹² x 50 x 50 = 150 x 10⁻¹⁰ = 1.5 x 10⁻⁸ J 1
- Show that the force on each plate of a parallel plate capacitor has a magnitude equal to \(\frac { 1 }{ 2 }\) QE, where Force = 1 / 2 QE Work done = 1 / 2 V x Q The physical origin of the factor 1 / 2 in the force formula lies in the fact that just outside the... 2
- A μ piF capacitor is charged by a 200 V supply. It is then disconnected from the supply C₁ = 4 x 10⁻⁶F V = 200 V C₂ = 2 x 1o⁻⁶F E₁ = 1 / 2 C₁V² = 1 / 2 x 4 x 10⁻⁶ x 200 x 200 = 8 x 1o⁻² Q = C₁V = 4 x 10⁻⁶ x 200 = 8 x 10⁻⁴ C E₂ =... 1
- (a) Are potential difference and potential energy the same? (b) If they are not the same, then define them. (a) No. The potential difference is a field property. Potential energy is the interaction energy of charge configuration. (b) The electrosta... 1
- A proton and an electron move between two points having a potential difference V. (a) Both gain the same energy Work done = energy gain = Potential difference x Charge The p.d and charge are the same for each. (b) One eV i... 1
- ‘Work is done on the charge ’. What do you understand by this? While moving the charge, work is to be done against repulsion of the field. 1
- What is the potential difference between the surface and interior point of the charged conductor? The potential at every point in a charged conductor is the same and is equal to the potential on the surface. Therefore the potential differ... 1
- How can we increase the capacitance of a conductor? By increasing the linear dimension. 2
- How will the applied voltage be divided among the capacitors? In a series combination, the applied voltage divides among the capacitors in inverse proportion to their capacitances: V ∝ 1/C . In series,... 1
- In which form and where is the energy of the capacitor stored? Electrical energy and is stored between the plates in the form of the electric field. 1
- Classify the following molecules into (a) Polar and non-polar. (H2O, H2, NH3, N2, CO2, CO, HCl, O2) (a) Polar molecules: H2O, NH3, CO, HCl Non-polar molecules: H2, N2, CO2, and O2 (b) polar and non-polar molecules: A molecule is said to be... 1
- Two copper spheres of radii, one hollow and the other solid are charged to the same potential. Both will hold the same charge No The capacity is small 2
- How much work is done in moving a 500 pC charge between two points on an equipotential surface? zero the work done in moving the given charge between two equipotential surfaces is equal to zero. 1