(a) (i) Two point charges 5μC and −1μC are placed at points (−3 cm,0,0) and (3 cm,0,0) respectively. An external electric field E=r2Ar^ where A=3×105 Vm is switched on in the region. Calculate the change in electrostatic energy of the system due to the electric field.
(ii) A system of two conductors is placed in air and they have net charge of +80μC and −80μC which causes a potential difference of 16 V between them.
1. Find the capacitance of the system.
2. If the air between the capacitor is replaced by a dielectric medium of dielectric constant 3, what will be the potential difference between the two conductors?
3. If the charges on two conductors are changed to +160μC and −160μC, will the capacitance of the system change? Give reason for your answer.
OR
(b) (i) Consider three metal spherical shells A, B and C, each of radius R. Each shell is having a concentric metal ball of radius R/10. The spherical shells A, B and C are given charges +6q, −4q, and 14q respectively. Their inner metal balls are also given charges −2q, +8q and −10q respectively. Compare the magnitude of the electric fields due to shells A, B and C at a distance 3R from their centres.
(ii) A charge −6μC is placed at the centre B of a semicircle of radius 5 cm, as shown in the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from B. A charge +5μC is moved from point 'C' to point 'A' along the circumference. Calculate the work done on the charge.
a. (a)(i) Two point charges 5μC and −1μC are placed at points (−3 cm,0,0) and (3 cm,0,0) respectively. An external electric field E=r2Ar^ where A=3×105 Vm is switched on in the region. Calculate the change in electrostatic energy of the system due to the electric field.
b. (a)(ii) A system of two conductors is placed in air and they have net charge of +80μC and −80μC which causes a potential difference of 16 V between them. (1) Find the capacitance of the system. (2) If the air between the capacitor is replaced by a dielectric medium of dielectric constant 3, what will be the potential difference between the two conductors? (3) If the charges on two conductors are changed to +160μC and −160μC, will the capacitance of the system change? Give reason for your answer.
c. OR: (b)(i) Consider three metal spherical shells A, B and C, each of radius R. Each shell is having a concentric metal ball of radius R/10. The spherical shells A, B and C are given charges +6q, −4q, and 14q respectively. Their inner metal balls are also given charges −2q, +8q and −10q respectively. Compare the magnitude of the electric fields due to shells A, B and C at a distance 3R from their centres.
d. (b)(ii) A charge −6μC is placed at the centre B of a semicircle of radius 5 cm, as shown in the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from B. A charge +5μC is moved from point 'C' to point 'A' along the circumference. Calculate the work done on the charge.