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An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ is
- a)π/3
- b)π/3 + tan⁻1√3/2
- c)3π/2
- d)tan⁻1√3/2
Correct answer is option 'B'. Can you explain this answer?
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An electric dipole is placed along the X-axis at the origin O. A point...
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An electric dipole is placed along the X-axis at the origin O. A point...
Concept:
When an electric dipole is placed along the X-axis, the electric field at a point P at a distance r from the origin can be calculated using the formula:
E = (1/4πε₀) * (2p cosθ) / r^3
Where p is the magnitude of the dipole moment, θ is the angle between the dipole moment and the line joining the dipole to the point, and r is the distance between the dipole and the point.
Given:
- The distance between the origin O and point P is 20 cm.
- The angle between OP and the X-axis is π/3.
Solution:
To find the angle θ that the electric field at point P makes with the X-axis, we need to consider the angle between the dipole moment and the line joining the dipole to the point. In this case, the angle between the dipole moment and the line OP is also π/3.
Using the formula for the electric field at point P and the given values, we have:
E = (1/4πε₀) * (2p cos(π/3)) / (0.2)^3
E = (1/4πε₀) * (2p * 1/2) / (0.008)
E = (1/4πε₀) * (p / 0.004)
The angle θ that the electric field at point P makes with the X-axis can be found using the components of the electric field in the X and Y directions:
tanθ = Ey / Ex
tanθ = E * sin(π/3) / E * cos(π/3)
tanθ = tan(π/3)
θ = π/3
Therefore, the correct answer is option (b) π/3 + tan⁻¹√3/2.
When an electric dipole is placed along the X-axis, the electric field at a point P at a distance r from the origin can be calculated using the formula:
E = (1/4πε₀) * (2p cosθ) / r^3
Where p is the magnitude of the dipole moment, θ is the angle between the dipole moment and the line joining the dipole to the point, and r is the distance between the dipole and the point.
Given:
- The distance between the origin O and point P is 20 cm.
- The angle between OP and the X-axis is π/3.
Solution:
To find the angle θ that the electric field at point P makes with the X-axis, we need to consider the angle between the dipole moment and the line joining the dipole to the point. In this case, the angle between the dipole moment and the line OP is also π/3.
Using the formula for the electric field at point P and the given values, we have:
E = (1/4πε₀) * (2p cos(π/3)) / (0.2)^3
E = (1/4πε₀) * (2p * 1/2) / (0.008)
E = (1/4πε₀) * (p / 0.004)
The angle θ that the electric field at point P makes with the X-axis can be found using the components of the electric field in the X and Y directions:
tanθ = Ey / Ex
tanθ = E * sin(π/3) / E * cos(π/3)
tanθ = tan(π/3)
θ = π/3
Therefore, the correct answer is option (b) π/3 + tan⁻¹√3/2.
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An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ isa)π/3b)π/3 + tan⁻1√3/2c)3π/2d)tan⁻1√3/2Correct answer is option 'B'. Can you explain this answer?
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An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ isa)π/3b)π/3 + tan⁻1√3/2c)3π/2d)tan⁻1√3/2Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ isa)π/3b)π/3 + tan⁻1√3/2c)3π/2d)tan⁻1√3/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ isa)π/3b)π/3 + tan⁻1√3/2c)3π/2d)tan⁻1√3/2Correct answer is option 'B'. Can you explain this answer?.
An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ isa)π/3b)π/3 + tan⁻1√3/2c)3π/2d)tan⁻1√3/2Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ isa)π/3b)π/3 + tan⁻1√3/2c)3π/2d)tan⁻1√3/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ isa)π/3b)π/3 + tan⁻1√3/2c)3π/2d)tan⁻1√3/2Correct answer is option 'B'. Can you explain this answer?.
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