Electrostatic Potential And Capacitance – Multiple Choice Questions

Q1. A Van de graph generator is used 

• to produce charged particle.
• to accelerate charged particles.
• to accelerate uncharged particles.
• to accelerate both charged and uncharged particles.

Solution

A Van de graph generator is used to accelerate charged particles.

Q2.

Positive mutual potential energy of a system containing two charges corresponds to

• Repulsion
• Attraction
• Could not predict
• None of the above

Solution

Yes, Negative mutual potential energy corresponds to attraction between two charges.

 

Q3.

Materials in which outer electrons are loosely bound and free to move within the metal at normal temperature are called

• Insulators
• Semiconductors
• Conductors
• Superconductors

Solution

In metallic conductors, the electrons of the outer shells of the atoms are loosely bound to the nucleus. They easily get detached from atom and move freely inside the metal.

Q4.

It requires 4 J of work to move a charge of 20 C from point A to point B, separated by a distance of 0.2 cm. The potential difference between A and B in volts

• 80
• 16
• 5
• 0.2

Solution

It requires 4 J of work to move a charge of 20 C from point A to point B, separated by a distance of 0.2 cm. The potential difference between A and B in volts

W = 4J

q = 4J

Work done = charge × potential difference

4 = 20 × potential difference

potential difference = 4 /20 = 0.2

Q5.

Choose the appropriate words to complete the sentence:

Equipotential surfaces are closer together in the region of fields and farther apart in the regions of fields.

• Weak, Strong
• Strong, Weak
• Parallel, Perpendicular
• Perpendicular, Parallel

Solution

Equipotential surfaces are closer together in the region of strong fields and farther apart in the regions of week fields.

Q6.

For any charge configuration, equipotential surface through a point is _____to the electric field at that point.

•   Parallel
• Perpendicular
• At 45°
• Anti-parallel.

Solution

Equipotential surface is always perpendicular to the electric field

because work done is moving a charge along an equipotential surface is zero.

This is possible only if the electric field is perpendicular to the equipotential surface.

 

Q7.

Negative mutual potential energy corresponds to attraction between two charges

• False
• True
• Can’t predict
• None of the above

Solution

Yes, Negative mutual potential energy corresponds to attraction between two charges.

 

Q8.

When a dielectric slab is introduced between the parallel plate capacitor, its capacitance

• increases
• decreases
• remains the same
• become zero.

Solution

Capacitance of a Parallel palte capacitor with a dieletric slab is given as,

Hence, it has been seen that C> C₀ that is on introduction of a dielectric slab in between the plates of a capacitor, its capacitances increases.

 

Q9.

The polarized dielectric is equivalent to

• two charged surfaces with induced surface charge densities
• one charged surface with induced surface charge density
• zero surface charge density
• non-zero volume charge density

Solution

Two charged surfaces are created and these have equal and opposite charge densities.

Q10.

Work done in carrying 2 C charge in a circular path of radius 2 m around a charge of 10 C is

• Zero
• 6.67J
• 15 J  
• 60J  

Solution

work done in moving a charge along a closed path is zero.

 

Q11.

Two capacitors of capacitance of 4 μF and 8 μFare connected in series with a battery. The voltage across the 4 μF is 2 V. Compute the total battery voltage.

• 3 V
• 2 V
• 5 V
• 1 V

Solution

In series arrangement of capacitors

 

Q12.

Direction of electric field on the equipotential surface is always

• Parallel to the surface
• At an angle of 45º to the surface
• Normal to the surface
• At an angle of 30º to the surface

Solution

Electric field is always normal to the equipotential surface at every point.

Q13.

In bringing an electron towards another electron, the electrostatic potential energy of the system

• remains same
• becomes zero
• increases
• decreases

Solution

P. E. = . As distance r decreases, potential energy increases.

Q14.

A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at the centre of the sphere is

• 0 V
• 10 V
• same as at point 5 cm away from the surface
• same as at point 25 cm away from the surface

Solution

Potential anywhere inside the hollow metal sphere is the same as that on the surface of a sphere.

Hence, the potential at the centre of the sphere is 10 V

Q15.

The displacement of charges inside the dielectric stops when

• the external field becomes maximum
• the external force on the charges of the molecules is balanced by the force due to internal fields
• the internal force on the charges of the molecules is balanced by the forces due to the internal fields
• none of the above

Solution

The displacement of charges inside the dielectric stops when the external force on the charges of the molecules is balanced by the force due to internal fields.

Q16.

A proton is accelerated from rest through a potential of 500 volts. Its final kinetic energy is

• 50 eV
• 500 eV
• 1000 eV
• 2000 eV

Solution

The change in potential energy is qV.

V = 500 V

Charge on proton, q = +1 e

dV = 500 × 1 = 500 eV

Q17.

How does the charge densities of conductors vary on an irregularly shaped conductor?

• High at sharp and less at flat portion
• Less at sharp and high at flat portion
• Remains constant
• Zero at sharp and high at flat portion

Solution

Sharp points have smaller radius of curvature and high charge density.

Q18.

Direction of electric field just outside the surface of a charged conductor is

• Parallel to the surface
• Normal to the surface
• Tangential to the surface
• At an angle of 45º to the surface.

Solution

If the electric field is not normal to the surface, then it will have a component along the surface which will immediately cause the flow of charges and produce surface current. But no current can exist under static conditions. Hence electric field is normal to the surface of the conductor at every point.

Q19.

Work done in placing a charge of 8 x 10^-18 C on a condenser of capacity 100 microfarad is

• 16 x 10^-32 J
• 3.1 x 10^-26 J
• 4 x 10^-10 J
• 32 x 10^-32 J

Solution

Given:

q = 8 x 10^-18 C

C = 100 μF

 

Q20.

Three different capacitors are connected in series, then:

• they will have equal charges
• they will have same potential
• both 1 & 2
• none of these

Solution

In series charge on each condenser is same.

Q21.

The distance between the plates of a capacitor is d. What will be the new capacitance if a metal plate of thickness d/2 is introduced between the plates without touching them

• remains the same
• it will be half of its initial value
• it will be double of its initial value
• it will be thrice of its initial value

Solution

Capacitance of a Parallel palte capacitor with a dieletric slab is given as,

When a metal plate of thickness d/2 is introduced between the plates without touching them then the new capacitance will be

Hence, the new capacitance will be double of its initial value.

Q22.

A uniformly polarized dielectric amounts to induced ______ charge density but no ______charge density.

• volume, line
• surface, volume
• volume, surface
• line, volume

Solution

As charges are separated on the surface of the dielectric but not in its interior volume.

Q23.

The external field induces dipole moment by

• only stretching
• only re-orienting
• stretching or re-orienting
• ionizing

Solution

The external field induces dipole moment by stretching or re-orienting

Q24.

The work done in moving a test charge over an equipotential surface is:

• 1
• Infinity
• 0
• -1

Solution

Work done is zero, as the potential difference is equal to zero.

Recall that work done = potential difference/ charge

Q25.

Electrostatic field is zero the conductor.

• outside
• Inside
• On the surface
• At the centre

Solution

When a conductor is placed in an electric field, its electrons start moving in the opposite direction to that of external electric field (). Due to this field, negative and positive charges are induced on two ends of the surface of the conductor. The process continues till the electric field () set up by the charges becomes equal and opposite to the external field. Hence, the net fieldinside the conductor will be zero.

Q26.

Coulomb’s law is given by F = kq₁q₂rⁿ, where n is

• 1 / 2
• 2
• - 2
• -1 / 2

Solution

Coulomb’s law is an inverse square law.

hence, n = -2

Q27.

Three capacitors of capacitances 3 μF are available. The minimum and maximum capacitances, which may be obtained, are

• 1 μF, 12 μF
• 1 μF,6 μF
• 1 μF, 9 μF
• 3 μF, 9 μF

Solution

When three capacitors connected in series then the capacitance is minimum.

When three capacitors connected in parallel then the capacitance is maximum.

Q28.

The amount of work done in moving a unit positive charge through distance of 10 cm on an equipotential surface is

• 10 cm
• 1/10 cm
• Zero
• 100 joule

Solution

Work done on equipotential surface is zero.

Q29.

A bird sitting on a bare power cable does not feel any shock because of

• Zero potential difference between its legs
• High potential difference between its legs
• Special property of its legs
• Low potential difference between its legs

Solution

Bird will not get a shock unless you complete the circuit to ground. Current passes only when there is difference in potential. So, a bird sitting on a bare power cable does not feel any shock because of absence of potential difference.

Q30.

Let Q denote the charge, V denote potential difference and U denote stored energy. Of these quantities, capacitors in parallel must have the same:

• Q only
• V only
• U only
• Q and V only

Solution

Because capacitors in parallel have the same potential difference across them.

Q31.

The electric field inside a dielectric decreases, when it is placed in an external electric field. This happens due to

• Electrostatic repulsion between atoms
• Electrostatic attraction between atoms
• Electrostatic shielding
• Polarization

Solution

In a dielectric, free movement of charges is not possible. So, the external field induces dipole moment by stretching or re-orienting molecules of the dielectric and makes it polarized. The collective effect of all the molecular dipole moments is net charges on the surface of the dielectric which produce a field that opposes the external field.

Q32.

Optical analogue of an equipotential surface is

• Wave motion of light
• Wavefront of light
• Interference of light
• Reflection of light

Solution

Wavefronts are surfaces of constant phase. Similarly, equipotential surface due to point charge is spherical in shape and has same potential at each point on selected surface.

Q33.

If a unit charge is taken from one part to another part over an equipotential surface, then what is the change in electrostatic potential energy of the charge?

• 1 J
• 10 J
• 100 J
• 0 J

Solution

As the potential of equipotent surface is constant, therefore the amount of work done could be, 

W = q (V_f – V_i)
= q ( V – V )
= 0 J

Q34.

Metallic sphere of radius R is charged to potential V. Then charge q is proportional to

• V
• R
• both V and R
• none

Solution

q = CV

Hence, The charge q is proportional to both V and R.

Q35.

Which of the following statements is not true for polar molecules?

• the centres of positive and negative charges are separated
• permanent dipole moment
• examples are oxygen and hydrogen molecules
• examples are HCl or water molecules

Solution

The oxygen and hydrogen molecules are non-polar molecules.

Q36.

The potential energy of a system containing only one point charge is

• Zero
• Infinity
• Nonzero finite
• None of the above

Solution

The electrostatic potential energy of a system containing only one point charge is zero, as no work is required to move the charged particle from infinity to its location.

Q37.

Electric field at the surface of a charged conductor is proportional to

• Volume of the sphere
• Area of the sphere
• Surface charge density
• Volume charge density

Solution

From the relation  we conclude that electric field at surface of a charged conductor is proportional to surface charge density σ.

Q38.

The extent of polarization depends on

• Dipole potential energy
• Thermal energy
• Dipole potential energy and thermal energy
• Kinetic energy of bound charges

Solution

The extent of polarization depends on the relative strength of two mutually opposite factors: the dipole potential energy in the external field tending to align the dipoles with the field and thermal energy tending to disrupt the alignment.

Q39.

Two capacitors of 20 μF and 30 μF  are connected in series to a battery of 40 V. Calculate charge on each capacitor.

• 500 C
• 478 C
• 480 C
• 450 C

Solution

C_s = 12 μF

Now, Q = C_s x V = 12 x 40 = 480 C

Q40.

Which of the following statement is not true for non-polar molecules?

• the centres of positive and negative charges coincide
• no permanent dipole moment
• examples are oxygen and hydrogen molecules
• examples are HCl or water molecules

Solution

The HCl and water molecules are polar molecules.                                

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