Objective questions

1. The electric field strength at distant point, P, due to a point charge, +q, located at the origin, is 100 µ V/m. If the point charge is now enclosed by a perfectly conducting metal sheet sphere whose center is at the origin, then the electric field strength at the point, P, outside the sphere, becomes

(a) Zero

 (b)100 µV/m

(c) – 100 µV/m

(d) 50 µV/m                                                                                                    [GATE 1995 : 1 Mark]

Sol: The point charge +q will induce a charge – q on the surface of metal sheet sphere. Using Gauss’s law, the net electric flux passing through a closed surface is equal to the charge enclosed = + q – q = 0 D = 0, E = 0 at point P. Option (a)

2. A metal sphere with 1 m radius and surface charge density of 10 Coulombs / m2 is enclosed in a cube of 10 m side. The total outward electric displacement normal to the surface of the cube is

(a) 40 π Coulombs

(b)10 π Coulombs

(c) 5 π Coulombs

 (d)None of the above

[GATE 1996: 1 Mark]

 Sol:. The sphere is enclosed in a cube of side = 10m. Using Gauss’s law, the net electric flux flowing out through a closed surface is equal to charge enclosed.

∯𝑫⃗ . 𝒅𝒂⃗= 𝑸(𝒆𝒏𝒄𝒍𝒐𝒔𝒆𝒅) = 𝑷𝑺 𝟒𝝅𝒓² = 𝟏𝟎 × 𝟒𝝅 = 𝟒𝟎𝝅 𝒄𝒐𝒖𝒍𝒐𝒎𝒃𝒔

Option (a)

3. In commercial TV transmission in India, picture and speech signals are modulated respectively (Picture) (Speech)

(a) VSB and VSB

(b)VSB and SSB

(c) VSB and FM

(d)FM and VSB

 [GATE 1990: 2 Marks]

 Soln. Note that VSB modulation is the clever compromise between SSB and DSB. Since TV bandwidth is large so VSB is used for picture transmission. Also, FM is the best option for speech because of better noise immunity

Option (c)