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Two point charges 10C and -10C are placed at a certain distance. What is the electric potential of their midpoint?
- a)Some positive value
- b)Some negative value
- c)Zero
- d)Depends on medium
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two point charges 10C and -10C are placed at a certain distance. What ...
Electric Potential at the Midpoint of Two Point Charges
To find the electric potential at the midpoint of two point charges, we can use the principle of superposition. The electric potential at a point due to multiple charges is the algebraic sum of the electric potentials due to each individual charge.
Calculating Electric Potential
The electric potential at a point due to a point charge is given by the equation:
V = k * q / r
Where:
- V is the electric potential
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- q is the charge
- r is the distance between the charge and the point where the potential is being calculated
In this scenario, we have two point charges: +10C and -10C. Let's assume the distance between them is 'd'. The midpoint is equidistant from both charges, so the distance from each charge to the midpoint is d/2.
Using the equation for electric potential, we can calculate the potential at the midpoint due to each charge separately:
V1 = k * (+10C) / (d/2)
V2 = k * (-10C) / (d/2)
Since the charges have equal magnitudes but opposite signs, their potentials will have equal magnitudes but opposite signs as well.
Applying Superposition Principle
To find the electric potential at the midpoint, we need to add the potentials due to each charge:
V_total = V1 + V2
Considering their magnitudes and opposite signs, we have:
V_total = (k * (+10C) / (d/2)) + (k * (-10C) / (d/2))
= (10C * k / (d/2)) - (10C * k / (d/2))
= 0
Conclusion
Therefore, the electric potential at the midpoint of two point charges of +10C and -10C is zero. This means that the potential at the midpoint is the same as if there were no charges present. The cancellation of potentials is a result of the equal but opposite charges and the symmetry of the arrangement.
Hence, the correct answer is option c) Zero.
To find the electric potential at the midpoint of two point charges, we can use the principle of superposition. The electric potential at a point due to multiple charges is the algebraic sum of the electric potentials due to each individual charge.
Calculating Electric Potential
The electric potential at a point due to a point charge is given by the equation:
V = k * q / r
Where:
- V is the electric potential
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- q is the charge
- r is the distance between the charge and the point where the potential is being calculated
In this scenario, we have two point charges: +10C and -10C. Let's assume the distance between them is 'd'. The midpoint is equidistant from both charges, so the distance from each charge to the midpoint is d/2.
Using the equation for electric potential, we can calculate the potential at the midpoint due to each charge separately:
V1 = k * (+10C) / (d/2)
V2 = k * (-10C) / (d/2)
Since the charges have equal magnitudes but opposite signs, their potentials will have equal magnitudes but opposite signs as well.
Applying Superposition Principle
To find the electric potential at the midpoint, we need to add the potentials due to each charge:
V_total = V1 + V2
Considering their magnitudes and opposite signs, we have:
V_total = (k * (+10C) / (d/2)) + (k * (-10C) / (d/2))
= (10C * k / (d/2)) - (10C * k / (d/2))
= 0
Conclusion
Therefore, the electric potential at the midpoint of two point charges of +10C and -10C is zero. This means that the potential at the midpoint is the same as if there were no charges present. The cancellation of potentials is a result of the equal but opposite charges and the symmetry of the arrangement.
Hence, the correct answer is option c) Zero.
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Two point charges 10C and -10C are placed at a certain distance. What ...
Electric potential is a scalar quantity and its value is solely dependent on the charge near it and the distance from that charge. In this case, the point is equidistant from the two point charges and the point charges have the same value but opposite nature. Therefore equal but opposite potentials are generated due to the charges and hence the net potential at midpoint becomes zero.
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