Exams Prep Master
Electrostatic Potential is a concept used in charges and potentials in physics. The work that is done by an external force in bringing a unit positive charge from infinity to that point is known as the electrostatic potential at that point. These concepts deal with currents and charges on a surface and are used to calculate the potential at a point or over a field of charges on a surface. An equipotential surface is a surface with a constant value of potential at all points on the surface. For a single charge q, the potential is given by V = q / 4πεor.
A capacitor is a system of two conductors that is separated by an insulator. A single conductor can also be used as a capacitor by assuming the other to be at infinity. A capacitor with fixed capacitance is symbolically shown as -||-, while the one with variable capacitance is shown as the following image given below. Now, let the potential difference V be the work done per unit positive charge in bringing a small test charge from one conductor to the other conductor against the field. Also, V is proportional to Q and the ratio Q/V is a constant,
C = Q / V
The constant C is called the capacitance of the capacitor. Capacitance is independent of Q or V.
Ques: A positively charged particle is released from rest in a uniform electric field. The electric potential energy of the charge
(a) remains constant because the electric field is uniform.
(b) increases because the charge moves along the electric field.
(c) decreases because the charge moves along the electric field.
(d) decreases because the charge moves opposite to the electric field.
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Ans: (c) decreases because the charge moves along the electric field.
Explanation: The electric potential energy of the charge decreases. This is due to the fact that the positively charged particle is influenced by some electrostatic force acting in the direction of the electric field. This is why the positively charged particle moves in the direction of the electric field. The positive work done on the electric field with the charge is given by the following-
W = - ðÂÂ>¥U where U is the potential energy
= - q ðÂÂ>¥V where q is the charge of the particle, and V is the potential difference
= q (Vinitial - Vfinal)
Thus, electric potential decreases, and hence, the electrostatic potential energy decreases too, according to the formula.
Ques: Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately
(a) spheres
(b) planes
(c) paraboloids
(d) ellipsoids
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Ans: (a) spheres
Explanation: An equipotential surface is a surface with a constant value of the potential at all points on the surface. For a single charge q, the potential is given by
V = q / 4πεor
Now, from a great distance, a collection of charges always seems like a single point charge. Thus, if viewed from a great distance the equipotential surface due to a point charge (which is actually a collection of charges) are usually spherical.
Ques: What is the dimension of the dipole moment?
(a) [I L T]
(b) [I L T-1]
(c) [I L2 T]
(d) [I T]
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Ans: (a) [I L T]
Explanation: The formula defining dipole moment is given by,
dipole moment = charge separation x length of the dipole. The electric charge, q has dimensions [I T] and length has dimensions [L]. Therefore, the dipole moment has the dimension [I T L] and has unit C m or C*cm.
Ques: Why is water not used as a dielectric between the plates of a capacitor?
(a) dielectric constant is very low
(b) dielectric strength is very low
(c) dielectric constant is very high
(d) dielectric strength is very high
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Ans: (b) dielectric strength is very low
(c) dielectric constant is very high
Explanation: The dielectric constant of water is very high which is why it has very low dielectric strength. This property of water does not allow water to be used as a dielectric between the plates of a capacitor due to complications.
Ques: The electric potential V at any point O (x, y, z all in metres) in space is given by V = 4x2 volt. The electric field at the point (1 m, 0, 2 m) in volt/metre is
(a) 8 along negative x-axis
(b) 8 along positive x-axis
(c) 16 along negative x-axis
(d) 16 along positive z-axis
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Ans: (a) 8 along negative x-axis.
Explanation: The electric field at a point is given by, E = - dV / dx. The negative sign is an indication that electrostatic potential is inversely affected by the electric field, which means if the electric field increases in the same direction in which electrostatic potential decreases. Now, V is the electric potential at any point O given in space by the equation, V = 4x2 volt.
So, V = 4x2 volt.
And, E = - dV / dx.
Substituting V in the equation for E,
E = - d(4x2) / dx.
Thus, E = - 8x volt/metre.
Thus, electric field at point (1 m, 0, 2 m) is - 8x volt/metre i.e. 8 along the negative x-axis.
Ques: If a unit positive charge is taken from one point to another over an equipotential surface, then
(a) work is done on the charge.
(b) work is done by the charge.
(c) work done is constant.
(d) no work is done.
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Ans: (d) no work is done.
Explanation: An equipotential surface is a surface with a constant value of the potential at all points on the surface. For a single charge q, the potential is given by
V = q / 4πεor
If a unit positive charge is taken from one point to the other the electric field over the equipotential surface would be normal to the surface of the charges where the potential exists. Thus, the work done in this case would be zero.
Ques: A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V. The potential at the centre of the sphere is
(a) 0 V
(b) 10 V
(c) Same as at point 5 cm away from the surface
(d) Same as at point 25 cm away from the surface
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Ans: (b) 10 V.
Explanation: The potential on the surface of the hollow metal sphere with a 5 cm radius is 10 V. It is known that the potential inside the hollow sphere is the same as that of the potential on the surface. Thus, the potential at the centre of the hollow metal sphere which is charged is 10 V.
Ques: The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A is
(a) proportional to the square root of the distance between the plates.
(b) linearly proportional to the distance between the plates.
(c) independent of the distance between the plates.
(d) inversely proportional to the distance between the plates.
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Ans: (c) independent of the distance between the plates.
Explanation: A capacitor is a system of two conductors that is separated by an insulator. Let potential difference V be the work done per unit positive charge in bringing a small test charge from one conductor to the other conductor against the field. Also, V is proportional to Q and the ratio Q/V is a constant,
C = Q / V
The constant C is called the capacitance of the capacitor. Capacitance is independent of Q or V. The capacitance of a parallel plate capacitor is given by the formula,
C = ε (A / d)
where ε represents the absolute permittivity of the dielectric material being used. The dielectric constant, ε0 also called the permittivity of free space and has a value of 8.854 x 10-12 Farads per metre.
But the capacitance of an isolated parallel plate capacitor is different and the force between the plates is given by the formula = Q2 / 2Aε0. Therefore, it has no relation to the distance between the plates.
Ques: A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system
(a) increases by a factor of 4.
(b) decreases by a factor of 2.
(c) remains the same.
(d) increases by a factor of 2.
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Ans: (b) decreases by a factor of 2.
Explanation: A capacitor when connected with another uncharged capacitor in parallel changes the electrostatic potential. The electrostatic potential is given by
V2 = V / 2.
We know that the electrostatic potential energy is given by the formula,
U = (1/2) CV2.
Substituting, the value of V2 we get that the electrostatic potential energy is decreasing by a factor of 2.
Ques: A conductor with a positive charge
(a) is always at +ve potential.
(b) is always at zero potential.
(c) is always at negative potential.
(d) may be at +ve, zero or -ve potential.
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Ans: (d) may be at positive, zero, or negative potential.
Explanation: The potential of a conductor with a positive charge can be at positive, zero, or negative potential. It is dependent upon the fact how one defines the zero potential of the conductor.
Ques: Which of the following options is correct? If a conductor has a potential V 4 - 0 and there are no charges anywhere else outside, then
(a) there must not 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) there must be charges inside the surface.
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Ans: (b) there cannot be any charge in the body of the conductor.
Explanation: The charge in a closed charged conductor always resides on the outer surface of the conductor. Even if a conductor has a potential of V 4 - 0 and there are no charges on the outside, therefore, no charge in the body of a conductor should be present. Thus, there cannot be any charge in the body of the conductor.
Ques: Three charges Q, +q and +q are placed at the vertices of an equilateral triangle of side l as shown in the figure. If the net electrostatic energy of the system is zero, then Q is equal to
(a) -q
(b) +q
(c) zero
(d) - q/2
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Ans: (d) - q/2.
Explanation: We know that C is inversely proportional to distance.
C ∝ 1/d
Cmedium / Cair = d / (d - t + t/K) where K is the di-electric constant.
Calculating using the formula we get - q/2.
Ques: 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 these
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Ans: (d) None of these.
Explanation: If a conductor has a surface which is an equipotential surface, and the electric field outside the surface of a conductor is perpendicular to the surface and if the conductor carries a charge and it is always uniformly distributed over the surface of the conductor, then the conductor is a perfect conductor and can conduct electric charges easily and effectively. Thus, all these statements are false.
Ques: 64 drops each having the capacity C and potential V are combined to form a big drop. If the charge on the small drop is q, then the charge on the big drop will be
(a) 2q
(b) 4q
(c) 16q
(d) 64q
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Ans: (d) 64q.
Explanation: The relation between charge and potential in terms of a capacitor C
is given by the formula,
Q = CV.
where q is the charge on the small drop and V is the potential.
Now all the drops hold capacitance, C, therefore, we hold a total of 64 drops creating the big drop, later the total capacitance of the big drop would be 64C and thus, the charge on the big drop will be 64q.
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Ques: An example of an equipotential surface in the earth is
- A line passes through the centre of the earth connecting two points along the diameter.
- A plane that passes through the circular section of the hemisphere of the earth.
- A spherical surface at a distance of 1 km from the surface of the earth with its centre at the centre of the earth.
- A plane on the surface of the earth, which is a tangent to the earth.
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Ans: (c) A spherical surface at a distance of 1 km from the surface of the earth with its centre at the centre of the earth.
Explanation: An equipotential surface is a surface with a constant value of the potential at all points on the surface. In a spherical object or surface, the potential is found constant at all points. Therefore, a spherical surface at a distance of 1 km from the surface of the earth with its centre at the centre of the earth is a correct example of an equipotential surface.
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