An isolated 16 μF parallel plate air capacitor has a potential differences of 1000 V (Figure 5 a). A dielectric slab having relative permittivity (i.e. dielectric constant) = 5 is introduced to fill the space between the two plates com pletely. (Figure 5 b). Calculate:
(i) The new capacitance of the capacitor.
(ii) The new potential differences between the two plates of the capacitor
An electron revolves around the nucleus of hydrogen atom in a circular orbit of radius 5 x 10-11 m. Calculate
(i) Intensity of electric field of the nucleus at the position of the electron.
(ii) Electrostatic potential energy of the hydrogen nucleus and electron system.
In the circuit shown below, PQ is a uniform metallic wire of length 4 m and resistance 20 Ω. Battery B has an emf of 10V and internal resistance of 1 Ω. J is a jockey or slide contact. Resistance of the ammeter and connecting wires is negligible.
(i) When the jockey J does not touch the wire PQ, what is the reading of ammeter A?
(ii) Where should the jockey J be pressed on the wire PQ so that the galvanometer G shows no deflection?
(i) When the jockey is not touched then the resistance of 10 ohm will not apply to the circuit therefore X and Y are in series and PQ is parallel to both of them and circuit will be changed as
Rxy =1 + 4 = 5 ohm
Reading of Ammeter will be 2.5 A.
(ii) The circuit can be rearranged in the following way.
Let B be point where jockey is touched therefore this point is a null point so the circuit will represent a wheat stone’s bridge.
The resistance per unit length = 5 ohm / meter
Then according to wheat stone’s bridge,
PR / PB = RQ / BQ
RPB = X x 5,
RBQ = (4 - x) x 5
1 / x x 5 = 4 / (4 - x) x 5 5(4 - x) = 20 x
20 - 5 x = 20 x
20 =25 x
x = 20/25 = 0.8 m
PB = 0.8 m
BQ = 4-0.8 = 3.2 m
The jockey should be pressed at a distance of 3.2 m so that there is no deflection.
(i) What is the effect of each of the magnetic fields on the needle?
(ii) When the needle is in equilibrium, obtain an expression for an angle θ made by the needle with in terms
of only.