An electric dipole consists of two opposite charges of magnitude $q = 1 \times {10^{ - 6\;}}$ C separated by 2.0 cm. the dipole is placed in an external field of $1 \times {10^5}$ ${\rm{N}}{{\rm{C}}^{ - 1}}$. What maximum torque does the field exert on the dipole? How much work must an external agent do to turn the dipole end for end, starting from position of alignment (${\rm{\theta }} = {0^0}$)

$2 \times {10^{ - 3\;}}{\rm{N}} - {\rm{m}},\;4 \times {10^{ - 3}}{\rm{\;J}}$

$4.4 \times {10^{6\;}}{\rm{N}} - {\rm{m}},\;3.2 \times {10^{ - 4}}{\rm{\;J}}$

$ - 2 \times {10^{3\;}}{\rm{N}} - {\rm{m}},\; - 4 \times {10^3}{\rm{\;J}}$

$4 \times {10^{3\;}}{\rm{N}} - {\rm{m}},2 \times {10^{ - 3}}{\rm{\;J}}$

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NEET • PHYSICS • ELECTRIC POTENTIAL AND CAPACITANCE

Electric potential and capacitance practice · Mixed difficulty

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151 Medium

151 of 245

Analyzing +4 | -1

Assertion:- When charges are shared between two parallel plate capacitors, charge of system is conserved but some energy is lost.
Reason:- During the sharing of charges, some energy is dissipated as heat.

View answer and explanation

Correct option: A

If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion

If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion because charge is conserved, but energy is lost as heat due to resistance in connecting wires during charge sharing.

152 Medium

152 of 245

Analyzing +4 | -1

Assertion: A parallel plate capacitor is connected across battery through a key. A dielectric slab of dielectric constant

{k}

is introduced between the plates. The energy stored becomes

{k}

times.
Reason: The surface density of charge on the plate remains constant.

View answer and explanation

Correct option: C

If assertion is true but reason is false

Option C (If assertion is true but reason is false) is correct because the surface charge density changes when a dielectric is inserted with the battery connected.

153 Medium

153 of 245

Application +4 | -1

ABC

is an equilateral triangle of side

2m

. If

\overrightarrow E = 10\,\,N{C^{ - 1}}

then

{V_A} - {V_B}

View answer and explanation

Correct option: B

- 10V

Option B (

- 10V

) is correct because the potential difference is calculated as

V_A - V_B = -E \cdot d

, where d is the displacement vector from B to A.

154 Medium

154 of 245

Understanding +4 | -1

Torque acting on an electric dipole in a uniform electric field is maximum if the angle between p and E is

View answer and explanation

Correct option: C

90°

Option C (90°) is correct because the torque on an electric dipole is maximum when the angle between the dipole moment and the electric field is 90 degrees.

155 Medium

155 of 245

Application +4 | -1

The capacitance of an air capacitor is

15\mu F

the separation between the parallel plates is

6mm.

A copper plate of

3mm

thickness is introduced symmetrically between the plates. The capacitance now becomes

View answer and explanation

Correct option: D

30\mu F

Option D (

30\mu F

) is correct because inserting a copper plate reduces the effective distance between the plates, increasing the capacitance.

156 Medium

156 of 245

Understanding +4 | -1

A soap bubble is given a negative charge, then its radius

View answer and explanation

Correct option: B

Increases

Option B is correct because the negative charge on the soap bubble will cause repulsion between the charges, increasing the surface area and thus the radius.

157 Medium

157 of 245

Understanding +4 | -1

Three capacitors of capacity

{C_1},{C_2},{C_3}

are connected in series. Their total capacity will be

View answer and explanation

Correct option: C

{\left( {C_1^{ - 1} + C_2^{ - 1} + C_3^{ - 1}} \right)^{ - 1}}

Option C is correct. The total capacitance of capacitors in series is the inverse of the sum of the inverses of individual capacitances.

158 Medium

158 of 245

Analyzing +4 | -1

Identify the WRONG statement

View answer and explanation

Correct option: C

The electrical potential energy of a proton electron system will increase if the separation between the two is increased

Option C (The electrical potential energy of a proton electron system will increase if the separation between the two is increased) is the WRONG statement because increasing the separation between a proton and electron decreases the potential energy (which is negative).

159 Easy

159 of 245

Application +4 | -1

The capacity of a parallel plate condenser consisting of two plates each 10 cm square and are separated by a distance of 2 mm is [Take air as the medium between the plates]

View answer and explanation

Correct option: D

4.42 \times {10^{ - 12}}\,\,F

Option D (

4.42 \times {10^{ - 12}}\,F

) is correct because it is the result of calculating the capacitance of a parallel plate capacitor using the given dimensions and the permittivity of air.

160 Medium

160 of 245

Understanding +4 | -1

Which among the following represents the expression of displacement current during charging of a capacitor? (Symbols have their usual meaning)

View answer and explanation

Correct option: D

All of these

Option D (All of these) is correct because all the given expressions are valid representations of the displacement current during the charging of a capacitor.

161 Medium

161 of 245

Application +4 | -1

The work done in carrying a charge of

5\mu C

from a point

A

to a point

B

in an electric field is

10mJ

. The potential difference

\left( {{V_B} - {V_A}} \right)

is then

View answer and explanation

Correct option: B

- 2kV

Option B (- 2kV) is correct because the potential difference is calculated using the formula

W = q(V_B - V_A)

, where W is the work done and q is the charge.

162 Medium

162 of 245

Application +4 | -1

The plates of a parallel plate condenser are pulled apart with a velocity

v.

If at any instant their mutual distance of separation is

d,

then the magnitude of the time of rate of change of capacity depends on

d

as follows

View answer and explanation

Correct option: B

1/{d^2}

Option B (

1/{d^2}

) is correct because the rate of change of capacitance is inversely proportional to the square of the distance between the plates.

163 Easy

163 of 245

Understanding +4 | -1

A positively charged particle is released from rest in an uniform electric field. The electric potential energy of the charge

View answer and explanation

Correct option: C

Decreases because the charge moves along the electric field

Option C is correct because a positively charged particle moves along the electric field from a region of higher potential to lower potential, thus decreasing its electric potential energy.

164 Medium

164 of 245

Analyzing +4 | -1

Considering a group of positive charges, which of the following statements is correct?

View answer and explanation

Correct option: A

Net potential of the system cannot be zero at a point but net electric field can be zero at that point.

Option A is correct because the electric potential is a scalar quantity and cannot be zero if all charges are positive, while the electric field is a vector quantity and can be zero due to cancellation.

165 Medium

165 of 245

Remembering +4 | -1

The capacity of parallel plate condenser depends on

View answer and explanation

Correct option: D

The separation between the plates

Option D (The separation between the plates) is correct because the capacitance of a parallel plate capacitor is inversely proportional to the distance between the plates.

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166 Easy

166 of 245

Analyzing +4 | -1

A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved farther apart by pulling at them by means of insulating handles, then

View answer and explanation

Correct option: D

The voltage across the capacitor increases

Option D (The voltage across the capacitor increases) is correct because when the plates are moved apart after disconnecting the battery, the charge remains constant, and the capacitance decreases, leading to an increase in voltage.

167 Medium

167 of 245

Understanding +4 | -1

The potential at a point due to an electric dipole will be maximum and minimum when the angles between the axis of the dipole and the line joining the point to the dipole are respectively

View answer and explanation

Correct option: D

{0^\mathrm{o}}

and

{180^\mathrm{o}}

Option D (

{0^\mathrm{o}}

and

{180^\mathrm{o}}

) is correct because the potential due to a dipole is maximum when the angle is 0 degrees and minimum when the angle is 180 degrees.

168 Medium

168 of 245

Understanding +4 | -1

The intensity of electric field at a point between the plates of a charged capacitor

View answer and explanation

Correct option: D

Does not depend upon the distance between the plates

Option D is correct. The electric field between the plates of a charged capacitor is uniform and does not depend on the distance between the point and the plates.

169 Medium

169 of 245

Application +4 | -1

0.2F

capacitor is charged to

600\;V

by a battery. On removing the battery, it is connected with another parallel plate condenser of

1F.

The potential decreases to

View answer and explanation

Correct option: A

100\;volts

Option A (100 volts) is correct because the total charge is conserved and redistributed between the two capacitors, leading to a new potential.

170 Medium

170 of 245

Application +4 | -1

Capacitance

\left( {\mathrm{in\;}F} \right)

of a spherical conductor with radius

1\;m

View answer and explanation

Correct option: A

1.1 \times {10^{ - 10}}

Option A is correct. The capacitance of a spherical conductor is given by C = 4πε₀r.

171 Medium

171 of 245

Remembering +4 | -1

The value of electric potential at any point due to any electric dipole is

View answer and explanation

Correct option: D

k.\frac{{\vec p.\vec r}}{{{r^3}}}

Option D (

k.\frac{{\vec p.\vec r}}{{{{r^3}}}}

) is correct because the electric potential due to an electric dipole is proportional to the dot product of the dipole moment and the position vector, divided by the cube of the distance.

172 Medium

172 of 245

Understanding +4 | -1

On increasing the plate separation of a charged condenser, the energy

View answer and explanation

Correct option: A

Increases

Option A (Increases) is correct because increasing the plate separation increases the potential difference for a constant charge, thus increasing the energy stored.

173 Medium

173 of 245

Application +4 | -1

What is the potential energy of the equal positive point charges of

1\mu C

each held

1\;m

apart in air

View answer and explanation

Correct option: A

9 \times {10^{ - 3}}\;J

Option A (9 × 10^-3 J) is correct because the potential energy of two point charges is calculated using U = kQ1Q2/r.

174 Medium

174 of 245

Understanding +4 | -1

The potential to which a conductor is raised, depends on

View answer and explanation

Correct option: C

Both (1) and (2)

Option C (Both (1) and (2)) is correct because the potential of a conductor depends on both the amount of charge and the geometry and size of the conductor.

175 Medium

175 of 245

Application +4 | -1

An electric dipole consists of two opposite charges, each of magnitude 1.0

\mathrm{\mu }

C separated by a distance of 2.0 cm. the dipole is placed in an external electric field of

{10^5}

N{C^{ - 1}}

. The maximum torque on the dipole is

View answer and explanation

Correct option: C

\times {10^{ - 3}}

N-m

Option C (2

\times {10^{ - 3}}

N-m) is correct because it is the maximum torque calculated using the formula torque = dipole moment * electric field.

176 Medium

176 of 245

Application +4 | -1

A parallel plate air capacitor is charged to a potential difference of

V.

After disconnecting the battery, distance between the plates of the capacitor is increased using an insulating handle. As a result, the potential difference between the plates

View answer and explanation

Correct option: B

Increases

Option D (

5 \times {10^7}

) is correct because the electric field is the energy gained divided by the charge and the mean free path.

177 Medium

177 of 245

Understanding +4 | -1

The electric potential inside a conducting sphere

View answer and explanation

Correct option: C

Remains constant from centre to surface

Option C is correct because the electric field inside a conductor is zero, so the potential is constant and equal to the potential at the surface.

178 Medium

178 of 245

Application +4 | -1

An electric dipole consists of two opposite charges of magnitude

q = 1 \times {10^{ - 6\;}}

C separated by 2.0 cm. the dipole is placed in an external field of

1 \times {10^5}

\mathrm{N}{\mathrm{C}^{ - 1}}

. What maximum torque does the field exert on the dipole? How much work must an external agent do to turn the dipole end for end, starting from position of alignment (

\mathrm{\theta } = {0^0}

)

View answer and explanation

Correct option: D

2 \times {10^{ - 3\;}}\mathrm{N} - \mathrm{m},\;4 \times {10^{ - 3}}\mathrm{\;J}

Option D (

2 \times {10^{ - 3\;}}\mathrm{N} - \mathrm{m},\;4 \times {10^{ - 3}}\mathrm{\;J}

) is correct because it accurately calculates the maximum torque and work done using the electric dipole moment and electric field.

179 Medium

179 of 245

Application +4 | -1

An electric dipole of moment

p

is placed in the position of stable equilibrium in uniform electric field of intensity

E.

It is rotated through an angle

\theta

from the initial position. The potential energy of electric dipole in the final position is

View answer and explanation

Correct option: D

- pE\cos \theta

Option D (

- pE\cos \theta

) is correct because the potential energy of a dipole in an electric field is given by

U = -pE \cos \theta

, where

\theta

is the angle between the dipole moment and the electric field.

180 Easy

180 of 245

Understanding +4 | -1

Two spheres of unequal radii are supplied with equal quantity of charges. The potential will

View answer and explanation

Correct option: B

Be more on the smaller sphere

Option B is correct because the electric potential is inversely proportional to the radius, so the smaller sphere will have a higher potential.

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