The electric field lines of a positive charge is as shown in figure: Give the sign of potential difference V p - V q .

We know, The potential V for a point charge decreases with distance and the potential at infinity is chosen to be zero. In this question the point P is nearer then the point Q . Therefore, The potential at point P is V P which greater than the potential V Q at point Q . So, V P - V Q = Positive sign.

Three capacitors of capacitances 2 pF , 3 pF and 4 pF are connected in parallel. c Determine the charge on each capacitor if the combination is connected to a 100 V supply.

Given, The supply voltage, V = 100 V . The capacitors C 1 = 2 pF , C 2 = 3 pF and C 3 = 4 pF . As they are in parallel, the voltage across them is the same. The relation between the charge ( q ) on a capacitor ( C ) and the potential difference ( V ) is, q = V C The charge on the first capacitor is, q 1 = V C 1 = 100 × 2 = 200 pF = 2 × 1 0 - 10 C The charge on the second capacitor is, q 2 = V C 2 = 100 × 3 = 300 pF = 3 × 1 0 - 10 C The charge on the third capacitor is, q 3 = V C 3 = 100 × 4 = 400 pF = 4 × 1 0 - 10 C

Three capacitors of capacitances 2 pF , 3 pF and 4 pF are connected in parallel. b Calculate the effective capacitance of the combination.

Given, the capacitance of the capacitors are C 1 = 2 pF , C 2 = 3 pF and C 3 = 4 pF The equivalent capacitance of the parallel combination C e q is given by the relation, C e q = C 1 + C 2 + C 3 = 2 + 3 + 4 = 9 pF Thus, the equivalent capacitance of the parallel combination is 9 pF .

How does the magnetic energy stored in an inductor and electrostatic energy stored in a capacitor related to their respective field strengths?

Energy stored in Inductor is directly proportional to magnetic field and Energy stored in capacitor is directly proportional to Electric field. Capacitor:- Capacitor is a device that stores electrostatic energy in the form of electric field. Energy stored in capacitor is given by E C = 1 2 CV 2 . Where C and V are capacitance and potential difference respectively. Also, V = Ed , Where E is electric field and d is distance between the capacitor plate. So, Energy stored in the capacitor is E C = 1 2 C Ed 2 . ⇒ E C ∝ E 2 So, Electrostatic Energy stored in capacitor is directly proportional to Electric field. Inductor:- Inductor is a device that stores magnetic energy in the form of magnetic field. Energy stored in inductor is given by E L = 1 2 Li 2 = μ 0 N 2 Ai 2 2 l . Where L is inductance and i is current in the circuit. ⇒ E L = 1 2 Li 2 = μ 0 N 2 Ai 2 2 l ⇒ E L = μ 0 N 2 A 2 l Bl μ 0 N 2 ⇒ E L = B 2 2 μ 0 Al Where L = μ 0 N 2 A 2 l and B = μ 0 Ni l . ⇒ E L ∝ B 2 So, Magnetic energy stored in inductor is directly proportional to magnetic field.