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Two identical charges (Q each) are separated by a certain distance. A third charge q is placed on the line joining the two charges, such that all the three charges are in equilibrium. What is the magnitude of the third charge?
- a)q = Q
- b)q = Q/4
- c)q = Q/2
- d)q = Q/3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two identical charges (Q each) are separated by a certain distance. A...
Explanation:
To solve this problem, we can use the principle of superposition. According to this principle, the net force on a charge due to a system of charges is equal to the vector sum of the individual forces on that charge due to each individual charge in the system.
We have two identical charges (Q each) separated by a certain distance. Let's consider the charges as Q1 and Q2 and the distance between them as d. The third charge (q) is placed on the line joining the two charges.
Step 1: Calculate the force on the third charge due to each of the identical charges.
The force between two charges is given by Coulomb's law:
F = k * (|q1| * |q2|) / r^2
where F is the force between the charges, k is the electrostatic constant, |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
The force on the third charge due to Q1 can be calculated as:
F1 = k * (|Q1| * |q|) / (d/2)^2
Since the charges are in equilibrium, the net force on the third charge must be zero. Therefore, the force on the third charge due to Q2 must be equal in magnitude and opposite in direction to the force due to Q1.
Step 2: Equate the forces and solve for the magnitude of the third charge.
F2 = -F1 (opposite direction)
k * (|Q2| * |q|) / (d/2)^2 = -k * (|Q1| * |q|) / (d/2)^2
|Q2| = -|Q1|
Since the charges Q1 and Q2 are identical, |Q2| = |Q1| = Q.
Therefore, -Q = Q
This implies that Q = 0.
Step 3: Calculate the magnitude of the third charge.
From the above equation, we have:
|Q| = |q| / 4
|q| = 4|Q|
Therefore, the magnitude of the third charge is q = Q/4.
Hence, the correct answer is option 'B': q = Q/4.
To solve this problem, we can use the principle of superposition. According to this principle, the net force on a charge due to a system of charges is equal to the vector sum of the individual forces on that charge due to each individual charge in the system.
We have two identical charges (Q each) separated by a certain distance. Let's consider the charges as Q1 and Q2 and the distance between them as d. The third charge (q) is placed on the line joining the two charges.
Step 1: Calculate the force on the third charge due to each of the identical charges.
The force between two charges is given by Coulomb's law:
F = k * (|q1| * |q2|) / r^2
where F is the force between the charges, k is the electrostatic constant, |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
The force on the third charge due to Q1 can be calculated as:
F1 = k * (|Q1| * |q|) / (d/2)^2
Since the charges are in equilibrium, the net force on the third charge must be zero. Therefore, the force on the third charge due to Q2 must be equal in magnitude and opposite in direction to the force due to Q1.
Step 2: Equate the forces and solve for the magnitude of the third charge.
F2 = -F1 (opposite direction)
k * (|Q2| * |q|) / (d/2)^2 = -k * (|Q1| * |q|) / (d/2)^2
|Q2| = -|Q1|
Since the charges Q1 and Q2 are identical, |Q2| = |Q1| = Q.
Therefore, -Q = Q
This implies that Q = 0.
Step 3: Calculate the magnitude of the third charge.
From the above equation, we have:
|Q| = |q| / 4
|q| = 4|Q|
Therefore, the magnitude of the third charge is q = Q/4.
Hence, the correct answer is option 'B': q = Q/4.
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Community Answer
Two identical charges (Q each) are separated by a certain distance. A...
Suppose the charge q is placed somewhere between the two charges.
For equilibrium of charge q, resultant force on q should be zero.
r1 = r2 = r
So, the charge q should be placed midway between the two charges.
For equilibrium of the system, resultant force on each charge is zero.
So, the resultant force on Q = 0
Magnitude of the charge q = Q/4
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Two identical charges (Q each) are separated by a certain distance. A third charge q is placed on the line joining the two charges, such that all the three charges are in equilibrium. What is the magnitude of the third charge?a)q = Qb)q = Q/4c)q = Q/2d)q = Q/3Correct answer is option 'B'. Can you explain this answer?
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