Potential Due to an Electric Dipole MCQ Quiz - Objective Question with Answer for Potential Due to an Electric Dipole - Download Free PDF

Concept:

Electric potential:

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

Dipole moment:

• When two equal and opposite charges are separated by a small distance then this combination of charges is called an electric dipole.
• The multiplication of charge and the distance between them is called an electric dipole moment.
• The electric dipole moment is denoted by P and the SI unit of dipole moment is Coulombmeter (Cm).
• The direction electric dipole moment is from negative charge to positive charge.

Dipole moment = P = 2qa

Where q is charge and 2a is the distance between two charged particles.

Electric potential Due to dipole:

Case-1 On the axis of the dipole

Case-2 On the perpendicular bisector of dipole

Where 

Where ϵ₀ = Permittivity of Substance 

Explanation: 

As dipole is a vector quantity, we can divide it into two perpendicular components,

• Along the direction of the point, where the potential to be calculated
• Perpendicular to the direction

Not potential 

The correct answer is - 1.6 × 10⁻²⁹ C m

Key Points

• Electric dipole moment
  • The electric dipole moment (p" id="MathJax-Element-71-Frame" role="presentation" style="position: relative;" tabindex="0">pp $\mathbf{p}$ ) is defined as the product of the charge (q" id="MathJax-Element-72-Frame" role="presentation" style="position: relative;" tabindex="0">qq $q$ ) and the separation distance (d" id="MathJax-Element-73-Frame" role="presentation" style="position: relative;" tabindex="0">dd $d$ ) between the charges.
  • Formula: p=q×d" id="MathJax-Element-74-Frame" role="presentation" style="position: relative;" tabindex="0">p=q×dp=q×d $\mathbf{p} = q \times d$
• Given values
  • Charge of an electron/proton (q" id="MathJax-Element-75-Frame" role="presentation" style="position: relative;" tabindex="0">qq $q$ ) = 1.6×10−19" id="MathJax-Element-76-Frame" role="presentation" style="position: relative;" tabindex="0">1.6×10−191.6×10−19 $1.6 \times 10^{-19}$ C
  • Separation distance (d" id="MathJax-Element-77-Frame" role="presentation" style="position: relative;" tabindex="0">dd $d$ ) = 1Å" id="MathJax-Element-78-Frame" role="presentation" style="position: relative;" tabindex="0">1Å1Å $1 \, \text{Å}$ = 1×10−10" id="MathJax-Element-79-Frame" role="presentation" style="position: relative;" tabindex="0">1×10−101×10−10 $1 \times 10^{-10}$ m
• Calculation
  • Using the formula p=q×d" id="MathJax-Element-80-Frame" role="presentation" style="position: relative;" tabindex="0">p=q×dp=q×d $\mathbf{p} = q \times d$ :
  • p=1.6×10−19C×1×10−10m" id="MathJax-Element-81-Frame" role="presentation" style="position: relative;" tabindex="0">p=1.6×10−19C×1×10−10mp=1.6×10−19C×1×10−10m $\mathbf{p} = 1.6 \times 10^{-19} \, \text{C} \times 1 \times 10^{-10} \, \text{m}$
  • p=1.6×10−29C⋅m" id="MathJax-Element-82-Frame" role="presentation" style="position: relative;" tabindex="0">p=1.6×10−29C⋅mp=1.6×10−29C⋅m $\mathbf{p} = 1.6 \times 10^{-29} \, \text{C} \cdot \text{m}$
• Final answer
  • The electric dipole moment is 1.6×10−29C⋅m" id="MathJax-Element-83-Frame" role="presentation" style="position: relative;" tabindex="0">1.6×10−29C⋅m1.6×10−29C⋅m $1.6 \times 10^{-29} \, \text{C} \cdot \text{m}$

Additional Information

• Dipole Moment Units
  • The SI unit for electric dipole moment is Coulomb-meter (C m).
  • In some contexts, dipole moments are also expressed in Debye units (D), where 1D=3.33564×10−30C⋅m" id="MathJax-Element-84-Frame" role="presentation" style="position: relative;" tabindex="0">1D=3.33564×10−30C⋅m1D=3.33564×10−30C⋅m $1 \, \text{D} = 3.33564 \times 10^{-30} \, \text{C} \cdot \text{m}$ .
• Significance of Electric Dipole Moment
  • The electric dipole moment is a measure of the separation of positive and negative charges in a system.
  • It is a vector quantity, having both magnitude and direction.
  • Dipole moments are crucial in understanding the behavior of molecules in electric fields, influencing physical and chemical properties.
• Applications of Dipole Moments
  • In physics and chemistry, dipole moments help in determining the polarity of molecules.
  • They are used in spectroscopy to understand the interaction of matter with electromagnetic fields.
  • Dipole moments are also key in fields like material science and molecular biology for studying molecular interactions.

Concept:

Work done against the conservative force =  - Δ PE

Potential due to a dipole at point is given by:

Calculation:

 = p ẑ 

Potential Energy at (a,0,0):

 = 0 

Potential Energy at (0,0,a):

Δ PE = 

Work done against the Electric field will be:

W = -Δ PE = 

∴ The amount of work required to move a charge ‘q’ from the point (a, 0, 0) to the point (0, 0, a) is  

CONCEPT   :

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

• Given that r >> a, where 2a is the distance between the two charges of the dipole
• The dipole moment is 

• ​Potential due to a dipole with dipole moment  at a point P having position vector  with respect to the dipole moment orientation is given by (if r >> a)

• There the potential falls off due to a factor of .

Therefore option 2 is correct.

CONCEPT:

Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

Assume:

• +q is placed at (a,0)
• -q is placed at (-a,0)

Potential at P(0,c,d) due to charge q placed at point A(a,0) is:

 (since the distance between points A and D is  )

Potential at P(0,c,d) due to charge -q placed at point B(-a,0) is:

Total potential at P due to both charges placed at points A and B is:

⇒  V = VPA + VPB 

 .

Therefore option 4 is correct.

Shortcut Trick

Equal and opposite charges are placed on A(a,0) and B(-a,0). Also point P(0,c,d) is equidistant from A and B. Therefore the potential on P due to charges placed on A and B will be equal in magnitude but opposite in sign. Thus the total potential due to the two charges on D will be zero.

CONCEPT   :

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

• Given that r >> a, where 2a is the distance between the two charges of the dipole
• The dipole moment is 

• ​Potential due to a dipole with dipole moment  at a point P having position vector  with respect to the dipole moment orientation is given by (if r >> a)

• There the potential falls off due to a factor of .

Therefore option 2 is correct.

CONCEPT   :

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

• Potential due to a dipole with dipole moment  at a point P(r,θ) having position vector  with respect to the dipole moment orientation is given by (if r >> a):

EXPLANATION:

• Given:
  • The dipole is placed at the origin

• The dipole moment is

​

• The position vector of point P is 
•  Potential due to a dipole with dipole moment  at a point P with position vector  with respect to the dipole moment orientation is given by (if r >> a)

Therefore option 2 is correct.

CONCEPT:

Electric dipole

• When two equal and opposite charges are placed at a very small distance to each other then this arrangement is called an electric dipole. 
• The electric dipole moment is defined as the product of the magnitude of one charge and the distance between the charges in an electric dipole.

⇒ P = q × 2r    

Where 2r = distance between the two charges

CALCULATION:

• The electric potential at a point due to an electric dipole is given as,

     -----(1)

where θ = angle between the line joining the point with the center of the dipole and the axial line of the dipole

For the equatorial plane,

And we know that,

⇒ cos 90 = 0

• So, the electric potential at the equatorial point of a small dipole with dipole moment p (at a distance r from the dipole) is given as,

• Hence option 1 is correct.

CONCEPT:

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

CONCEPT   :

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

• The potential due to a dipole is given by

• Where, 
  • p is the magnitude of dipole moment

​​​

• • θ is the angle between the dipole moment and 
  • Here  is the position vector of point P where potential is to be calculated
• Therefore the potential due to the dipole is

• Therefore option 3 is correct

CONCEPT:

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

• Potential due to a dipole with dipole moment  at a point P(r,θ) having position vector  with respect to the dipole moment orientation is given by (if r >> a):

• Therefore the potential can be calculated if p and r are known.

Therefore option 3 is correct.

CONCEPT:

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

• Assume:
  • +5 μC is placed at A(1,0)
  • -5 μC is placed at B(-1,0)
• Potential at P(3,0) due to charge 5 μC placed at point A(1,0) is

• Potential at P(3,0) due to charge -5 μC placed at point A(-1,0) is

• Total potential at D due to both charges placed at points A and B is:

⇒  V = VDA + VDB = 2250 - 1125  = 1125 V.

Therefore option 2 is correct.

CONCEPT: 

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

• Potential at D(d,0) due to charge q placed at point A(a,0) is:

• Potential at D(d,0) due to charge -q placed at point B(-a,0) is:

• Total potential at D due to both charges placed at points A and B is:

⇒  V = VDA + VDB 

• Since d >> a,

⇒  d² - a² ≈ d²

Therefore option 1 is correct.

CONCEPT:

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

• Potential due to a single charged particle Q at a distance r from it is given by:

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

• The potential due to a dipole is given by

• At the axial point, θ is zero, hence cosθ = 1, V is non-zero.
• At the equatorial point, θ is , hence cosθ = 0, V is zero.
• Therefore option 3 is correct