Four equal point charges Q each are placed in the xy-plane at (0, 2), (4, 2), (4, -2) and (0, -2). The work required to put a fifth charge Q at the origin of the coordinate system will be

$\frac{{{Q^2}}}{{4\pi {\varepsilon _0}}}$

$\frac{{{Q^2}}}{{4\pi {\varepsilon _0}}}\left( {1 + \frac{1}{{\sqrt 3 }}} \right)$

$\frac{{{Q^2}}}{{2\sqrt 2 \pi {\varepsilon _0}}}$

$\frac{{{Q^2}}}{{4\pi {\varepsilon _0}}}\left( {1 + \frac{1}{{\sqrt 5 }}} \right)$

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a would be

$\frac{Q}{{4\pi {\varepsilon _0}\left( {{\rm{a}} + {\rm{b}} + {\rm{c}}} \right)}}$

$\frac{{Q\left( {{a^2} + {b^2} + {c^2}} \right)}}{{4\pi {\varepsilon _0}\left( {{a^3} + {b^3} + {c^3}} \right)}}$

$\frac{{Q\left( {a + b + c} \right)}}{{4\pi {\varepsilon _0}\left( {{a^2} + {b^2} + {c^2}} \right)}}$

$\frac{Q}{{4\pi {\varepsilon _0}\left( {{\rm{a}} + {\rm{b}} + {\rm{c}}} \right)}}$

$\frac{Q}{{12\pi {\varepsilon _0}}}\frac{{ab + bc + ca}}{{abc}}$

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be:

${\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_4}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_3}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}$

${\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_3}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_4}} \right)}}{{{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}}}$

${\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_2}} \right)\left( {{{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}$

${\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_2}} \right)\left( {{{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}{{{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}}}$

${\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_4}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_3}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}$

A uniformly charged ring of radius 3a and total charge q is placed in xy -plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed v at z = 4a. The minimum value of v such that it crosses the origin is:

$\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{1}{{15}}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}$

$\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{4}{{15}}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}$

$\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{1}{5}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}$

$\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{2}{{15}}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}$

$\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{1}{{15}}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}$

A point dipole $\vec p = - {p_0}\hat x$ is kept at the origin. The potential and electric field due to this dipole on the y -axis at a distance ‘d’ are, respectively: (Take V = 0 at infinity)

$0,\frac{{\vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}$

$\frac{{\left| {\vec p} \right|}}{{4\pi {\epsilon_0}{{\rm{d}}^2}}},\frac{{\vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}$

$0,\frac{{ - \vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}$

$0,\frac{{\vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}$

$\frac{{\left| {\vec p} \right|}}{{4\pi {\epsilon_0}{{\rm{d}}^2}}},\frac{{ - \vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}$

29 + Mcqs in Electric Potential in Electromagnetic Theory Page 1 McqOptions

1.	What is the potential difference between 10sinθcosφ/r2 at A(1,30,20) and B(4,90,60)?
A.	2.386
B.	3.386
C.	4.386
D.	5.386
Answer» D. 5.386

2.	Given E = 40xyi + 20x2j + 2k. Calculate the potential between two points (1,-1,0) and (2,1,3).
A.	105
B.	106
C.	107
D.	108
Answer» C. 107

3.	Find the potential of V = 60sin θ/r2 at P(3,60,25)
A.	5.774
B.	6.774
C.	7.774
D.	8.774
Answer» B. 6.774

4.	A solid metal cube of edge length 2 cm is moving in a positive Y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive Z-direction. The potential difference between the two faces of the cube perpendicular to the X-axis is
A.	2 mV
B.	12 mV
C.	6 mV
D.	1 mV
Answer» C. 6 mV

5.	From the given list, name the item that is not a natural resource.
A.	Electricity
B.	Water
C.	Air
D.	Soil
Answer» B. Water

6.	Electric potential at a point with position vector r due to a point charge Q placed at the origin is given by the formula _____________.
A.	V = Q/ (2πєor2)
B.	V = Q/(4πєor2)
C.	V = Q/(4πєor)
D.	V = Q/(2πєor)
Answer» D. V = Q/(2πєor)

7.	_______________________ of charge 'q' at a point is the work done by the external force in bringing the charge 'q' from infinity to that point.
A.	Electric potential
B.	Electric field
C.	Kinetic energy
D.	Electrostatic potential energy
Answer» E.

8.	Four equal point charges Q each are placed in the xy-plane at (0, 2), (4, 2), (4, -2) and (0, -2). The work required to put a fifth charge Q at the origin of the coordinate system will be
A.	\(\frac{{{Q^2}}}{{4\pi {\varepsilon _0}}}\)
B.	\(\frac{{{Q^2}}}{{4\pi {\varepsilon _0}}}\left( {1 + \frac{1}{{\sqrt 3 }}} \right)\)
C.	\(\frac{{{Q^2}}}{{2\sqrt 2 \pi {\varepsilon _0}}}\)
D.	\(\frac{{{Q^2}}}{{4\pi {\varepsilon _0}}}\left( {1 + \frac{1}{{\sqrt 5 }}} \right)\)
Answer» E.

9.	Assuming there are no other charges, the work done in bringing a charge q2 from infinity to a distance r12 from charge q1 is ______________.
A.	q1q2/(4πεor)
B.	q1q2/(4πεor2)
C.	q1q2/√(4πεor)
D.	q1q2/√(4πεor2)
Answer» B. q1q2/(4πεor2)

10.	A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a would be
A.	\(\frac{{Q\left( {{a^2} + {b^2} + {c^2}} \right)}}{{4\pi {\varepsilon _0}\left( {{a^3} + {b^3} + {c^3}} \right)}}\)
B.	\(\frac{{Q\left( {a + b + c} \right)}}{{4\pi {\varepsilon _0}\left( {{a^2} + {b^2} + {c^2}} \right)}}\)
C.	\(\frac{Q}{{4\pi {\varepsilon _0}\left( {{\rm{a}} + {\rm{b}} + {\rm{c}}} \right)}}\)
D.	\(\frac{Q}{{12\pi {\varepsilon _0}}}\frac{{ab + bc + ca}}{{abc}}\)
Answer» C. \(\frac{Q}{{4\pi {\varepsilon _0}\left( {{\rm{a}} + {\rm{b}} + {\rm{c}}} \right)}}\)

11.	A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be:
A.	\({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_3}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_4}} \right)}}{{{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}}}\)
B.	\({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_2}} \right)\left( {{{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}\)
C.	\({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_2}} \right)\left( {{{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}{{{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}}}\)
D.	\({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_4}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_3}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}\)
Answer» D. \({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_4}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_3}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}\)

12.	A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is
A.	560 pJ
B.	508 pJ
C.	692 pJ
D.	600 pJ
Answer» C. 692 pJ

15.	In free space, a particle A of charge 1 μC is held fixed at a point P. Another particle B of the same charge and mass 4 μg is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is:[\({\rm{Take}}\;\frac{1}{{4{\rm{\pi }}{_0}}} = 9 \times {10^9}{\rm{\;N}}{{\rm{m}}^2}{{\rm{C}}^{ - 2}}\)]
A.	1.0 m/s
B.	3.0 × 104 m/s
C.	2.0 × 103 m/s
D.	1.5 × 102 m/s
Answer» D. 1.5 × 102 m/s

17.	An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10-29 C-m. What is the potential energy of the electric dipole?
A.	-9 × 10-20 J
B.	-10 × 10-29 J
C.	-20 × 10-18 J
D.	-7 × 10-27 J
Answer» E.

19.	An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5 Ω. The value of R to give a potential difference of 5 mV across 10 cm of potentiometer wire is
A.	395 Ω
B.	495 Ω
C.	490 Ω
D.	480 Ω
Answer» B. 495 Ω

13.	Electrostatic potential at a distance 'r' from a point charge 'q' is proportional to?
A.	1 / r
B.	1 / r2
C.	r
D.	r2
Answer» B. 1 / r2

14.	A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of -4 Q, the new potential difference between the same two surfaces is:
A.	-2 V
B.	2 V
C.	4 V
D.	V
Answer» E.

16.	A uniformly charged ring of radius 3a and total charge q is placed in xy -plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed v at z = 4a. The minimum value of v such that it crosses the origin is:
A.	\(\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{4}{{15}}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}\)
B.	\(\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{1}{5}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}\)
C.	\(\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{2}{{15}}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}\)
D.	\(\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{1}{{15}}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}\)
Answer» D. \(\sqrt {\frac{2}{{\rm{m}}}} {\left( {\frac{1}{{15}}\frac{{{{\rm{q}}^2}}}{{4\pi {\varepsilon _0}{\rm{a}}}}} \right)^{1/2}}\)

18.	A point dipole \(\vec p = - {p_0}\hat x\) is kept at the origin. The potential and electric field due to this dipole on the y -axis at a distance ‘d’ are, respectively: (Take V = 0 at infinity)
A.	\(\frac{{\left\| {\vec p} \right\|}}{{4\pi {\epsilon_0}{{\rm{d}}^2}}},\frac{{\vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}\)
B.	\(0,\frac{{ - \vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}\)
C.	\(0,\frac{{\vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}\)
D.	\(\frac{{\left\| {\vec p} \right\|}}{{4\pi {\epsilon_0}{{\rm{d}}^2}}},\frac{{ - \vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}\)
Answer» C. \(0,\frac{{\vec p}}{{4\pi {\epsilon_0}{{\rm{d}}^3}}}\)

20.	WHAT_IS_THE_POTENTIAL_DIFFERENCE_BETWEEN_10SIN‚ÂÀ√≠‚ÄÖ√†√®COS‚ÂÀ√¨‚ÀÖ√∫/R²_AT_A(1,30,20)_AND_B(4,90,60)??$#
A.	2.386
B.	3.386
C.	4.386
D.	5.386
Answer» D. 5.386

21.	The_voltage_at_any_point_in_an_ac_circuit_will_be$
A.	Peak voltage
B.	RMS voltage
C.	Average voltage
D.	Source voltage
Answer» C. Average voltage

22.	The potential taken between two points across a resistor will b?
A.	Positive
B.	Negative
C.	Zero
D.	Infinity
Answer» C. Zero

23.	The potential difference in an open circuit is
A.	Zero
B.	Unity
C.	Infinity
D.	Circuit does not exist open
Answer» D. Circuit does not exist open

24.	Given E = 40xyi + 20x²j + 2k. Calculate the potential between two points (1,-1,0) and (2,1,3).
A.	105
B.	106
C.	107
D.	108
Answer» C. 107

25.	Find the potential of V = 60sin ‚âà√≠‚Äö√†√®/r² at P(3,60,25)$
A.	5.774
B.	6.774
C.	7.774
D.	8.774
Answer» B. 6.774

Explore topic-wise MCQs in Electromagnetic Theory.

What is the potential difference between 10sinθcosφ/r2 at A(1,30,20) and B(4,90,60)?

Given E = 40xyi + 20x2j + 2k. Calculate the potential between two points (1,-1,0) and (2,1,3).

Find the potential of V = 60sin θ/r2 at P(3,60,25)

A solid metal cube of edge length 2 cm is moving in a positive Y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive Z-direction. The potential difference between the two faces of the cube perpendicular to the X-axis is

From the given list, name the item that is not a natural resource.

Electric potential at a point with position vector r due to a point charge Q placed at the origin is given by the formula _____________.

_______________________ of charge 'q' at a point is the work done by the external force in bringing the charge 'q' from infinity to that point.

Four equal point charges Q each are placed in the xy-plane at (0, 2), (4, 2), (4, -2) and (0, -2). The work required to put a fifth charge Q at the origin of the coordinate system will be

Assuming there are no other charges, the work done in bringing a charge q2 from infinity to a distance r12 from charge q1 is ______________.

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a would be

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be:

A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is

Electrostatic potential at a distance 'r' from a point charge 'q' is proportional to?

A uniformly charged ring of radius 3a and total charge q is placed in xy -plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed v at z = 4a. The minimum value of v such that it crosses the origin is:

An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10-29 C-m. What is the potential energy of the electric dipole?

A point dipole \(\vec p = - {p_0}\hat x\) is kept at the origin. The potential and electric field due to this dipole on the y -axis at a distance ‘d’ are, respectively: (Take V = 0 at infinity)

An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5 Ω. The value of R to give a potential difference of 5 mV across 10 cm of potentiometer wire is

WHAT_IS_THE_POTENTIAL_DIFFERENCE_BETWEEN_10SIN‚ÂÀ√≠‚ÄÖ√†√®COS‚ÂÀ√¨‚ÀÖ√∫/R2_AT_A(1,30,20)_AND_B(4,90,60)??$#

The_voltage_at_any_point_in_an_ac_circuit_will_be$

The potential taken between two points across a resistor will b?

The potential difference in an open circuit is

Given E = 40xyi + 20x2j + 2k. Calculate the potential between two points (1,-1,0) and (2,1,3).

Find the potential of V = 60sin ‚âà√≠‚Äö√†√®/r2 at P(3,60,25)$

A point charge 0.4nC is located at (2, 3, 3). Find the potential differences between (2, 3, 3)m and (-2, 3, 3)m due to the charge.

Six equal point charges Q = 10nC are located at 2,3,4,5,6,7m. Find the potential at origin.

A point charge 2nC is located at origin. What is the potential at (1,0,0)?

Potential difference is the work done in moving a unit positive charge from one point to another in an electric field. State True/False.

WHAT_IS_THE_POTENTIAL_DIFFERENCE_BETWEEN_10SIN‚ÂÀ√≠‚ÄÖ√†√®COS‚ÂÀ√¨‚ÀÖ√∫/R²_AT_A(1,30,20)_AND_B(4,90,60)??$#

Given E = 40xyi + 20x²j + 2k. Calculate the potential between two points (1,-1,0) and (2,1,3).

Find the potential of V = 60sin ‚âà√≠‚Äö√†√®/r² at P(3,60,25)$

26.	A point charge 0.4nC is located at (2, 3, 3). Find the potential differences between (2, 3, 3)m and (-2, 3, 3)m due to the charge.
A.	2.5
B.	2.6
C.	2.7
D.	2.8
Answer» D. 2.8

27.	Six equal point charges Q = 10nC are located at 2,3,4,5,6,7m. Find the potential at origin.
A.	140.35
B.	141.35
C.	142.35
D.	143.35
Answer» E.

29.	Potential difference is the work done in moving a unit positive charge from one point to another in an electric field. State True/False.
A.	True
B.	False
Answer» B. False