Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 5

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Question 1
4 / -1

If a conductor has a potential V≠0 and there are no charges anywhere else outside, then

A
there must be charges on the surface or inside itself.

B
there cannot be any charge in the body of the conductor.

C
there must be charges only on the surface.

D
both (a) and (b) are correct.

Solution

If a conductor has a non zero potential and there are no charge anywhere else outside, then there must be charge on the surface of the conductor or inside the conductor. There cannot be any charge in the body of the conductor.
Question 2
4 / -1

Which of the following statements is false for a perfect conductor?

A
The surface of the conductor is an equipotential surface

B
The electric, field just outside the surface of a conductor is perpendicular to the surface

C
The charge carried by a conductor is always uniformly distributed over the surface of the conductor

D
None of the above

Solution

Since the electric field out of a conductor is perpendicular to the surface. Therefore, it will not have component along the surface of the conductor.
So, there will be no work done in moving the conductor along the surface.
So, it behaves as an equipotential surface.
The charge carried by the conductor is also uniformly distributed over the surface of the conductor.
Question 3
4 / -1

Consider two conducting spheres of radii R₁ and R₂ with R₁ > R₂. If the two are at the same potential, and the larger sphere has more charge than the smaller sphere, then

A
the charge density of smaller sphere is less then that of larger sphere.

B
the charge density of smaller sphere is more than that of larger sphere.

C
both spheres may have same charge density.

D
none of these.

Solution

Here V₁ = V₂ or
∴ q₁q₂ = R₁R₂ ......(i)
Given R₁ > R₂
∴ q₁ > q₂
∴ Larger sphere has more charge than the smaller sphere. Now charge densities.

As R₁> R₂ therefore σ₂ > σ₁
Charge density of smaller sphere is more thatn the charge density of large sphere.
Question 4
4 / -1

Two metal spheres, one of radius R and the other of radius 2R, both have the same surface density σ. If they are brought in contact and separated, then the new surface charge densities on each of the sphere are respectively

A

B

C

D

Solution

Before contact, Charges of each sphered,
q₁ = σ4πR²; q₂ = σ4π(2R)² = 4q₁
When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V₁= V₂

∴ q₂′ = 2q₁′....(i)
As there is no loss of charge in the process
∴ q₁′ + q₂′ = q₁ + q₂ = q₁ + 4q₁ = 5q₁ = 5(σ4πR²)
or q₁′ + 2q₁′ = 5σ4πR² (using (i))
Question 5
4 / -1

Two charged conducting spheres of radii a and b are connected to each other by a wire. The ratio of electric fields at the surfaces of two spheres is

A
a/b

B
b/a

C
a²/b²

D
b²/a²

Solution

Let q₁ and q₂ be the charges and C₁ and C₂ be the capacitance of two spheres
The charge flows from the sphere at higher potential to the other at lower potential, till their potentials becomes equal.
After sharing, the charges on two spheres would be
q₁/q₂ = C₁V/C₂V…(i)
Also C₁C₂ = ab…(ii)
From (i) q₁/q₂ = a/b
Ratio of surface charge on the two spheres
σ₁/σ₂ = q₁/4πa²⋅4πb²/q₂ = q₁/q₂⋅b₂/a₂= b/a(using(ii)
∴ The ratio of electric fields at the surfaces of two spheres E₁/E₂ = σ₁/σ₂ = b/a