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Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given by

  • a)
    V = p cos θ/4 π ∈₀ r2

  • b)
    V = p cos θ/4 π ∈₀ r

  • c)
    V = p sn θ/4 π ∈₀ r

  • d)
    V = 4p cos θ/ π ∈₀ r2

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two equal charges q of opposite sign separated by a distance 2a consti...
Explanation:

Electric Dipole and Potential:
- An electric dipole consists of two equal charges of opposite sign separated by a distance 2a.
- The dipole moment, denoted by p, is defined as the product of one of the charges and the separation distance: p = q * 2a.

Potential at Point P:
- To find the potential at point P, we can use the formula for the potential due to an electric dipole at a point on the axis.
- The potential V at point P is given by V = p * cos(θ) / (4 * π * ε₀ * r^2), where θ is the angle between the line joining the centre of the dipole to point P and the axis of the dipole.

Conclusion:
- Therefore, the correct option is A: V = p * cos(θ) / (4 * π * ε₀ * r^2).
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Most Upvoted Answer
Two equal charges q of opposite sign separated by a distance 2a consti...
Electric Dipole Potential Calculation
To calculate the potential at point P due to an electric dipole, we can use the formula:
\[ V = \dfrac{1}{4\pi\epsilon_0} \left( \dfrac{p\cos\theta}{r^2} \right) \]
where:
- \( V \) is the potential at point P
- \( p \) is the dipole moment
- \( \theta \) is the angle between the line joining the centre of the dipole to point P and the axis of the dipole
- \( r \) is the distance from the centre of the dipole to point P

Given Information
In this case, the potential at point P is given by:
\[ V = \dfrac{p\cos\theta}{4\pi\epsilon_0 r^2} \]
Given that the charges are equal and opposite, the dipole moment \( p \) is given by:
\[ p = 2qa \]
where:
- \( q \) is the charge
- \( a \) is the separation distance

Substitute Dipole Moment into Potential Formula
Substitute the expression for the dipole moment into the potential formula:
\[ V = \dfrac{2qa\cos\theta}{4\pi\epsilon_0 r^2} \]
Simplify the expression:
\[ V = \dfrac{qa\cos\theta}{2\pi\epsilon_0 r^2} \]
The final potential at point P due to the electric dipole is:
\[ V = \dfrac{p\cos\theta}{4\pi\epsilon_0 r^2} \]
Therefore, the correct answer is option 'A'.
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Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given bya)V = p cos θ/4 π ∈ r2b)V = p cos θ/4 π ∈ rc)V = p sn θ/4 π ∈ rd)V = 4p cos θ/ π ∈ r2Correct answer is option 'A'. Can you explain this answer?
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Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given bya)V = p cos θ/4 π ∈ r2b)V = p cos θ/4 π ∈ rc)V = p sn θ/4 π ∈ rd)V = 4p cos θ/ π ∈ r2Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given bya)V = p cos θ/4 π ∈ r2b)V = p cos θ/4 π ∈ rc)V = p sn θ/4 π ∈ rd)V = 4p cos θ/ π ∈ r2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given bya)V = p cos θ/4 π ∈ r2b)V = p cos θ/4 π ∈ rc)V = p sn θ/4 π ∈ rd)V = 4p cos θ/ π ∈ r2Correct answer is option 'A'. Can you explain this answer?.
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