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Find the angle at which the potential due a dipole is measured, when the distance from one charge is 12cm and that due to other is 11cm, separated to each other by a distance of 2cm.
- a)15
- b)30
- c)45
- d)60
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Find the angle at which the potential due a dipole is measured, when t...
Answer: d
Explanation: Here, the two charges are separated by d = 2cm.
The distance from one charge (say Q1) will be R1 = 11cm. The distance from another charge (say Q2) will be R2 = 12cm. If R1 and R2 is assumed to be parallel, then R2 – R1 = d cos θ. We get 1 = 2cos θ and cos θ = 0.5. Then θ =
cos-1(0.5) = 60.
Explanation: Here, the two charges are separated by d = 2cm.
The distance from one charge (say Q1) will be R1 = 11cm. The distance from another charge (say Q2) will be R2 = 12cm. If R1 and R2 is assumed to be parallel, then R2 – R1 = d cos θ. We get 1 = 2cos θ and cos θ = 0.5. Then θ =
cos-1(0.5) = 60.
Most Upvoted Answer
Find the angle at which the potential due a dipole is measured, when t...
To find the angle at which the potential due to a dipole is measured, we can use the concept of the electric field and the distance between the charges.
Given:
Distance from one charge (q1) = 12 cm
Distance from the other charge (q2) = 11 cm
Separation between the charges (d) = 2 cm
1. Calculating the Electric Field:
The electric field due to a dipole at a point on the axial line can be calculated using the formula:
E = (k * p) / r^3
Where:
E is the electric field
k is the electrostatic constant (9 × 10^9 Nm^2/C^2)
p is the dipole moment (q * d)
r is the distance from the center of the dipole
2. Calculating the Angle:
The angle at which the potential is measured is the angle between the line joining the two charges and the line connecting the point of measurement to the center of the dipole.
Let's assume the line connecting the two charges is the x-axis, and the line connecting the point of measurement to the center of the dipole is the y-axis.
Using basic trigonometry, we can calculate the angle using the formula:
tan θ = y/x
Where:
θ is the angle
y is the perpendicular distance from the center of the dipole to the point of measurement
x is the distance between the two charges
In this case, y = 12 cm - 11 cm = 1 cm
x = 2 cm
Substituting the values into the formula, we get:
tan θ = 1 cm/2 cm
tan θ = 0.5
To find the angle, we take the inverse tangent (arctan) of the value:
θ = arctan(0.5)
Using a calculator, we find that θ is approximately 26.57 degrees.
Therefore, the correct answer is option 'D' (60 degrees) is incorrect. The correct answer is option 'B' (30 degrees).
Note: It is important to double-check the calculations and ensure the given values are accurate before concluding the final answer.
Given:
Distance from one charge (q1) = 12 cm
Distance from the other charge (q2) = 11 cm
Separation between the charges (d) = 2 cm
1. Calculating the Electric Field:
The electric field due to a dipole at a point on the axial line can be calculated using the formula:
E = (k * p) / r^3
Where:
E is the electric field
k is the electrostatic constant (9 × 10^9 Nm^2/C^2)
p is the dipole moment (q * d)
r is the distance from the center of the dipole
2. Calculating the Angle:
The angle at which the potential is measured is the angle between the line joining the two charges and the line connecting the point of measurement to the center of the dipole.
Let's assume the line connecting the two charges is the x-axis, and the line connecting the point of measurement to the center of the dipole is the y-axis.
Using basic trigonometry, we can calculate the angle using the formula:
tan θ = y/x
Where:
θ is the angle
y is the perpendicular distance from the center of the dipole to the point of measurement
x is the distance between the two charges
In this case, y = 12 cm - 11 cm = 1 cm
x = 2 cm
Substituting the values into the formula, we get:
tan θ = 1 cm/2 cm
tan θ = 0.5
To find the angle, we take the inverse tangent (arctan) of the value:
θ = arctan(0.5)
Using a calculator, we find that θ is approximately 26.57 degrees.
Therefore, the correct answer is option 'D' (60 degrees) is incorrect. The correct answer is option 'B' (30 degrees).
Note: It is important to double-check the calculations and ensure the given values are accurate before concluding the final answer.
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Find the angle at which the potential due a dipole is measured, when the distance from one charge is 12cm and that due to other is 11cm, separated to each other by a distance of 2cm.a)15b)30c)45d)60Correct answer is option 'D'. Can you explain this answer?
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