Electric Charges and Fields Test

Result

Electric Charges and Fields Test - 8

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Weekly Quiz Competition

Question 1
4 / -1

Match the following and find the correct option.

A
A - q, B - r, C - p

B
A - p, B - r, C - p

C
A - r, B - p, C - q

D
A - r, B - q, C - p

Solution

Linear charge density, λ = charge/length ; A → q
Surface charge density, σ = charge/area; B → r
Volume charge density, ρ = charge/volume; C → p
Question 2
4 / -1

A uniformly charged conducting sphere of 4.4m diameter has a surface charge density of 60 μC m^-2. The charge on the sphere is

A
7.3 x 10^-3C

B
3.7 x 10^-6C

C
7.3 x 10^-6C

D
3.7 x 10^-3C

Solution

Here D = 2r = 4.4 m,
or r = 2.2 m, σ = 60 μC m^-2
Charge on the sphere, q = σ x 4πr²
= 60 x 10^-6 x 4 x (22/7) x (2.2)² = 3.7 x 10^-3C.
Question 3
4 / -1

A metallic spherical shell has an inner radius R₁ and outer radius R₂. A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is

A
q/4πR²₁

B
-q/4πR²₁

C
q²/4πR²₂

D
q/4πR²₂

Solution

When a charge +q is placed at the centre of spherical cavity as shown in figure.
Charge induced on the inner surface of shell = - q ... (i)
Charge induced on the outer surface of shell = + q ... (ii)

∴ Surface charge dcnsity on the inner surface = -q/4πR²₁
Question 4
4 / -1

In the question number 3, the surface charge density on the outer surface is

A
-q/4πR²₁

B
q/4πR²₂

C
q²/4πR²₁

D
2q/4πR²₂

Solution

Surface charge density on the outer surface +q/4πR²₂ (Using (ii))
Question 5
4 / -1

A positive charge Q is uniformly distributed along a circular ring of radius R. A small test charge q is placed at the centre of the ring as shown in figure. Then

A
if q > 0, and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre.

B
if q < 0 and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring.

C
if q < 0 it will perform SHM for small displacement along the axis.

D
all of the above.

Solution

At the centre of the ring, E = 0 when a positive charge q > 0 is displaced away from the centre in the plane of the ring, say to the right, force of repulsion on q, due to charge on right half increases and due to charge on left half decreases. Therefore, charge q is pushed back towards the centre. So option (a) is correct.
When charge q is negative (q < 0), force is of attraction.
Therefore, charge q displaced to the right continues moving to the right till it hits the ring. Along the axis of the ring, at a distance r from the centre.
E = (Qr/(4πε₀(r² +a²)^3/2)
If charge q is negative (q < 0), it will perform SHM for small displacement along the axis.