Sairam

No. Lencho was not surprised to find a letter for him with money in it. He believed that God sent the money to him in answer to the letter he wrote to God.
However, upon receiving the money and counting it, he wrote another letter addressed to God advising him not to send the money through the mail because the money he received was less than the money he asked for. He thought that the employees in the post office took the missing amount.

The given figure shows six equal amount of charges, q, at the vertices of a regular hexagon.

Where, Charge, q = 5 µC = 5 × 10^{- 6} C

Side of the hexagon, l = AB = BC = CD = DE = EF = FA = 10 cm

Distance of each vertex from centre O, d = 10 cm

Electric potential at point O,

Where,

= Permittivity of free space

Therefore, the potential at the centre of the hexagon is 2.7 × 10⁶ V.

(b) What is the potential difference across each capacitor if the combination is connected to a 120 V supply?

Given, C₁ = C₂ = C₃ = 9 pF = 9 x 10^-12 F

V = 120 volt

a) Total capacitance of the series combination is given by

⇒ 

⇒ 

C_net = 3 x 10^-12 F = 3 pico-Farad.

(b) Let q be the charge on each capacitor.

Sum of the potential difference across the plates of the three capacitors must be equal to 120 V

⇒ V₁ + V₂ + V₃ = V_net

⇒  (∵ V_net = 120 V)

⇒ 

⇒ 

⇒ q = 360 x 10^-12 C

Therefore, potential difference across a capacitor

(c) At a point 18 cm from the centre of the sphere?

(a) Radius of the spherical conductor, r = 12 cm = 0.12 m

Charge is uniformly distributed over the conductor, q = 1.6 × 10 ^-7 C

Electric field inside a spherical conductor is zero. This is because if there is field inside the conductor, then charges will move to neutralize it.

(b) Electric field E just outside the conductor is given by the relation,

Where,

= Permittivity of free space

Therefore, the electric field just outside the sphere is 10⁵ N C^-1

(c) Electric field at a point 18 m from the centre of the sphere = E1

Distance of the point from the centre, d = 18 cm = 0.18 m

Therefore, the electric field at a point 18 cm from the centre of the sphere is .

4.4 x 10⁴ N/C