Electric Potential MCQ Quiz - Objective Question with Answer for Electric Potential - Download Free PDF

The correct answer is - V₀ > VA

Key Points

• Electric potential
  • In a uniform electric field pointing in the positive X direction, the electric potential decreases as we move in the direction of the field.
  • Since point A is at x = +2 cm and the field points in the positive X direction, the potential at A (VA) will be lower than the potential at the origin (V₀).
• Potential difference
  • The potential difference between two points in an electric field is given by V = Ed, where E is the electric field strength and d is the distance.
  • Since A is further from the origin in the direction of the electric field, V₀ > VA.

Additional Information

• Electric field direction
  • The direction of the electric field is defined as the direction in which a positive test charge would move.
  • In this case, the field points in the positive X direction, meaning it pushes positive charges in that direction.
• Potential at point B
  • Point B is on the Y axis at y = +1 cm.
  • Since the electric field is along the X axis, there is no change in potential along the Y axis.
  • Therefore, the potential at B (Vʙ) is the same as the potential at the origin (V₀).
• Electric field strength
  • The electric field strength E is uniform, meaning it has the same magnitude and direction at all points in the region.
  • This uniformity simplifies the calculation of potential differences as it depends only on the distance in the direction of the field.

Explanation:

Electric Potential Difference

Definition: The electric potential difference between two points in an electric field is defined as the work done to move a unit positive charge from one point to another. It is a measure of the potential energy per unit charge at a specific location in the field.

Formula: The electric potential difference (V) between two points is given by:

\( V = \frac{W}{Q} \)

where V is the electric potential difference, W is the work done, and Q is the charge.

Explanation:

When a charge moves in an electric field, work is done by or against the electric field. The amount of work done per unit charge is called the electric potential difference. This concept is analogous to gravitational potential difference, where work is done to move a mass in a gravitational field.

Units: The SI unit of electric potential difference is the volt (V). One volt is equivalent to one joule per coulomb (1 V = 1 J/C).

Correct Option Analysis:

The correct option is:

Option 1: Work done / charge

This option correctly describes the electric potential difference. The work done to move a charge from one point to another divided by the amount of charge gives the electric potential difference. Mathematically, this is represented as:

\( V = \frac{W}{Q} \)

where V is the electric potential difference, W is the work done, and Q is the charge.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: Electric charge / time

This option describes the concept of electric current, not electric potential difference. Electric current (I) is defined as the rate of flow of electric charge (Q) through a conductor per unit time (t). Mathematically, it is expressed as:

\( I = \frac{Q}{t} \)

The unit of electric current is the ampere (A).

Option 3: Charge × work done

This option does not represent any standard electrical quantity. Multiplying charge (Q) by work done (W) does not yield electric potential difference or any other commonly used electrical parameter.

Option 4: Work done / time

This option describes the concept of power, not electric potential difference. Power (P) is defined as the rate at which work (W) is done or energy is transferred per unit time (t). Mathematically, it is expressed as:

\( P = \frac{W}{t} \)

The unit of power is the watt (W).

Conclusion:

Understanding the distinction between different electrical concepts is crucial. The electric potential difference specifically refers to the work done to move a unit charge between two points in an electric field, and is accurately represented by the formula \( V = \frac{W}{Q} \). Other options describe different electrical quantities such as electric current and power, but do not pertain to electric potential difference.

Concept:

The work done in moving a charge q between two points in an electric field can be calculated using the formula:

W = q * (V_M - VN)

Where W is the work done, q is the charge, and V_M and V_N are the electric potentials at points M and N, respectively.

Since the points M and N are at the same distance from the charge Q, the potential at both points is the same:

V_M = V_N = 1 / (4πε₀) * Q / r

Thus, the difference in potential between the two points is:

V_M - V_N = 0

The work done in moving the charge between points M and N is given by:

W = (V_M - V_N) * q = 0

∴ The work done in moving the charge is 0 J.

Solution:

Let us first find the number of photons falling on the sphere.

E = n ×  (hC / λ)

n = (E × λ) / (hC)

n = (10^-7 × 200 × 10^-9) / (2 × 10^-25)

n = 10¹¹

Given that one in ten thousand ejects an electron.

Therefore, the total number of electrons ejected = (10¹¹ / 10⁴) = 10⁷

Total charge on the sphere = 10⁷ × 1.6 × 10^-19 = 1.6 × 10^-12 C

Potential = (K × Q) / R

Potential = (9 × 10⁹ × 1.6 × 10^-12) / (4.8 × 10^-2)

Potential = 3 × 10^-1 V

Calculation:
The potential V at a distance r from a charge Q is given by Coulomb's law:

V = kQ / r

For a square PQRS with a 100 µC charge at the center and side length 1 m, the distance from the center to any corner (the diagonal) is:

d = (√2) / 2

The potential at any corner due to the central charge is:

V = (9 × 10⁹ × 100 × 10^-6) / (√2 / 2) = 9√2 × 10⁵ V

Since the potential at point P and R same (the distance to the charge does not change), the potential difference ΔV between P and R is zero.

Therefore, the work done in moving a charge from P to R is:

Work = q . ΔV = q . 0 = 0

Concept:

• The electric potential difference between two points in an electric circuit carrying some current is the work done to move a unit charge from one point to the other.
• The standard metric unit on electric potential difference is the volt, abbreviated V. 
• The potential difference is the work done per unit charge.

Mathematically, it is defined as:

\(V={W\over Q}\)

V = Potential difference

W = Work done

Q = electric charge.

The S.I unit of work is joule and that of the charge is the coulomb.

Electric potential (V):

The capacity of a charged body to do work is called its electric potential. 

The greater the capacity of a charged body to do work, the greater is its electric potential.

Obviously, the work done to charge a body to 1 coulomb will be a measure of its electric potential
i.e., 

 \( V = \frac{W}{Q}\)

Where,

W is work done or potential energy in joule,

Q is charge in coulombs

∴ The unit of electric potential will be joules/coulomb or volt.

If  W = 1 joule, Q = 1 coulomb, then V = 1/1 = 1 volt.

Hence a body is said to have an electric potential of 1 volt if 1 joule of work is done to give it a charge of 1 coulomb. 

Calculaion:

Given:

2 C charge has 20 J potential energy

\( V = \frac{W}{Q}\)

∴ V = 20 / 2 = 10 V

The correct answer is option 3):(-240 × 10-19 J and 240 × 10-19 J)

Concept:

The work done by an external force to move a change from one point to another point is given

W = q ΔV

where

charge of electron

q = −1.6×10 ⁻¹⁹  C 

ΔV is the change in potential 

The electrostatic potential energy is

U = - W

Calculation:

q = −1.6×10 −19  C 

Potential at A is 60 V

Potential at  B is - 90 V

W = −1.6×10 −19( 60+ 90)

= - 240 ×10 −19 J

The electrostatic potential energy is

U = 240 ×10 −19 J

If a charge Q is moved from a point with electrostatic potential V₁ to another point with electrostatic potential V₂ then the work is done W is given by the formula:

 W= Q (V₂ - V₁) or

W = qV

Where q is the charge flowing, W is the work done and V is the potential difference.

Calculation:

As given work is done in moving a charge of 2 coulombs across two points having a potential difference of 5 volts.

q = 2 coulomb

V = 5 volt

⇒ W = qV

W = 2 × 5

W = 10 joule

Potential difference:

• It refers to the difference in electrical potential between two points in a circuit.
• The electric potential difference between two points in an electric circuit carrying some current is the work done to move a unit charge from one point to the other.
• The standard metric unit of electric potential difference is volt, abbreviated V. 

The potential difference is also defined as the work done per unit charge.

\(V={W\over Q}\)

Where V  Potential difference, W is Work done, and Q is electric charge.

The S.I unit of work is joule and that of the charge is the coulomb.

Additional Information 

• The potential difference is measured by Voltmeter.
• Ammeter is used to measure electric current.

• When a conductor is at equilibrium, the electric field inside it is always zero.
• Since the electric field is equal to the rate of change of potential, the voltage (potential) inside a conductor at equilibrium is constant at the value it reaches the surface of the conductor. 
• We take a charged conducting sphere as shown to understand this:

​          

The correct answer is Electrical Capacitance.

Key Points

• The Electrical Capacitance is expressed as the ratio of charge to a potential difference and its SI unit is Farad.
• Capacitance is expressed as the ratio of the electric charge on each conductor to the potential difference between them.
• The capacitance value of a capacitor is measured under Farad. The Farad is a large quantity of Capacitance.
• The capacitance of a conductor will be 1 farad if the charge of 1 coulomb raises the potential by 1 volt.

Important Points

Electrical Capacitance formula:

q = CV

q = charge

C = capacitance

V = voltage

Additional Information

Concept:

Electric Potential: It is the amount of work needed to move a unit charge from a reference point to a specific point against the electric field.

If the two points are specified then the total work done in moving the charge from one point to another with respect to the reference point charge is given as,

\(W=-\frac{1}{4\pi {{\epsilon }_{0}}}{{q}_{1}}{{q}_{2}}\left( \frac{1}{{{r}_{1}}}-\frac{1}{{{r}_{2}}} \right)=k{{q}_{1}}{{q}_{2}}\left( \frac{1}{{{r}_{2}}}-\frac{1}{{{r}_{1}}} \right)\)

Where, k = 9 × 109 N-m2 C-2

q1 and q2 = charges

r1 and r2 are distances

Electric Potential due to point charge: Consider a point charge is placed at the distance of ‘r’ from the charge ‘Q’ then the potential due to charge is,

\({{V}_{p}}=\frac{kQ}{r}\)

Calculation:

Given, q₁ = 1 μC, q₂ = 10 μC

Let r₁ be the distance the two-point charges one placed placed at (0, 0, 0) and other at (0, 10 , 0)

r₁ = 10 m

Let r₂ be the final distance between the two-point charges one placed at origin (0, 0, 0) and other at (5, 0, 0)

r₂ = 5 m

Total work done in moving the pont charge from (0, 0, 0) to (5, 0, 0) is

\(W=k{{q}_{1}}{{q}_{2}}\left( \frac{1}{{{r}_{2}}}-\frac{1}{{{r}_{1}}} \right)\)

\(W=9\times 10^9\times 10^{-11}\left( \frac{1}{5}-\frac{1}{10} \right)\)

W = 9 mJ

Concept:

The potential point charge at a distance r is defined as the amount of work done in moving that charge from infinite to the point from where it is calculated.

\(V = \frac{W}{Q}\)

W = work done

Q = Charge

And W = F.d

F = force

d = distance between point and charge = r

\(F = \frac{1}{{4\pi {\epsilon_0}}}\frac{{{Q_1}{Q_2}}}{{{r^2}}}\)

\( \Rightarrow W = \frac{1}{{4\pi {\epsilon_0}}}\frac{{{Q_1}{Q_2}}}{r}\)

\( \Rightarrow V = \frac{1}{{4\pi {\epsilon_0}}}\frac{Q}{r}\)

Calculation:

    \(V = {9 * 10^9 *5*10^{-6} \over 2}\)

        =22.5 KV

The correct answer is the same, opposite.Key Points

• In both cases, the induced potential differences are of the same magnitude.
• In case (a), the induced potential difference has the same sign as that of the magnet's north pole, i.e., it is positive.
• In case (b), the induced potential difference has the opposite sign as that of the magnet's south pole, i.e., it is negative.
• The magnitude of the induced potential difference depends on the rate of change of magnetic flux through the coil, which, in turn, depends on the speed and orientation of the magnet.
• The induced potential difference is given by the formula: V = -N du/dt, where V is the induced potential difference, N is the number of turns in the coil, and du/dt is the rate of change of magnetic flux through the coil.

Additional Information

• Induced potential difference refers to the voltage generated in a conductor when it is subjected to a changing magnetic field.
• An electric potential difference is created in the coil by the pace at which the number of magnetic field lines connected to the loop changes while the magnet and loop are moving relative to one another or by a change in current in a nearby conductor.
• The circuit resistance is inversely proportional to the induced current, and it is proportional to the induced electromotive force.
• Although there is no current when the circuit is open, there may be an induced electromotive force.