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Three point charges Q_{1} , - Q_{2} and Q_{3} are equally spaced along a line as shown in the figureIf the magnitudes of Q_{2} are equal, what must be the magnitude of Q_{3} in order that the net force on Q_{1} must be zero? Q_{1i} Q_{1} - Q_{2} Q_{3}?
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Three point charges Q_{1} , - Q_{2} and Q_{3} are equally spaced along...
Explanation:
Introduction:
In this problem, we need to find the magnitude of Q3 such that the net force on Q1 is zero. We can use Coulomb's law to calculate the force between two charges and then use the principle of superposition to find the net force on Q1 due to all three charges.
Calculating Force Between Charges:
The force between two charges Q1 and Q2, separated by a distance r, is given by Coulomb's law as:
F12 = k Q1 Q2 / r^2
where k is the Coulomb constant.
The force between Q1 and Q3 is also given by Coulomb's law as:
F13 = k Q1 Q3 / (2r)^2 = k Q1 Q3 / 4r^2
Since Q2 is negative, the force between Q1 and Q2 is attractive and is given by:
F12 = -k Q1 Q2 / r^2
Calculating Net Force on Q1:
To find the net force on Q1, we need to add up the forces due to Q2 and Q3. Since Q2 and Q3 are equally spaced from Q1, the horizontal components of the forces will cancel out and we only need to consider the vertical components.
The vertical component of the force between Q1 and Q2 is given by:
F12sinθ = -k Q1 Q2 sinθ / r^2
where θ is the angle between the line connecting Q1 and Q2 and the horizontal axis.
The vertical component of the force between Q1 and Q3 is given by:
F13sinθ = k Q1 Q3 sinθ / 4r^2
Since the forces due to Q2 and Q3 are in opposite directions, we can find the net force on Q1 as:
Fnet = F12sinθ + F13sinθ
Setting Fnet to zero and solving for Q3, we get:
Q3 = -Q2
Therefore, the magnitude of Q3 must be equal to the magnitude of Q2 for the net force on Q1 to be zero.
Conclusion:
In this problem, we used Coulomb's law to calculate the forces between charges and then used the principle of superposition to find the net force on Q1 due to all three charges. We found that the magnitude of Q3 must be equal to the magnitude of Q2 for the net force on Q1 to be zero.
Introduction:
In this problem, we need to find the magnitude of Q3 such that the net force on Q1 is zero. We can use Coulomb's law to calculate the force between two charges and then use the principle of superposition to find the net force on Q1 due to all three charges.
Calculating Force Between Charges:
The force between two charges Q1 and Q2, separated by a distance r, is given by Coulomb's law as:
F12 = k Q1 Q2 / r^2
where k is the Coulomb constant.
The force between Q1 and Q3 is also given by Coulomb's law as:
F13 = k Q1 Q3 / (2r)^2 = k Q1 Q3 / 4r^2
Since Q2 is negative, the force between Q1 and Q2 is attractive and is given by:
F12 = -k Q1 Q2 / r^2
Calculating Net Force on Q1:
To find the net force on Q1, we need to add up the forces due to Q2 and Q3. Since Q2 and Q3 are equally spaced from Q1, the horizontal components of the forces will cancel out and we only need to consider the vertical components.
The vertical component of the force between Q1 and Q2 is given by:
F12sinθ = -k Q1 Q2 sinθ / r^2
where θ is the angle between the line connecting Q1 and Q2 and the horizontal axis.
The vertical component of the force between Q1 and Q3 is given by:
F13sinθ = k Q1 Q3 sinθ / 4r^2
Since the forces due to Q2 and Q3 are in opposite directions, we can find the net force on Q1 as:
Fnet = F12sinθ + F13sinθ
Setting Fnet to zero and solving for Q3, we get:
Q3 = -Q2
Therefore, the magnitude of Q3 must be equal to the magnitude of Q2 for the net force on Q1 to be zero.
Conclusion:
In this problem, we used Coulomb's law to calculate the forces between charges and then used the principle of superposition to find the net force on Q1 due to all three charges. We found that the magnitude of Q3 must be equal to the magnitude of Q2 for the net force on Q1 to be zero.
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Three point charges Q_{1} , - Q_{2} and Q_{3} are equally spaced along a line as shown in the figureIf the magnitudes of Q_{2} are equal, what must be the magnitude of Q_{3} in order that the net force on Q_{1} must be zero? Q_{1i} Q_{1} - Q_{2} Q_{3}?
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Three point charges Q_{1} , - Q_{2} and Q_{3} are equally spaced along a line as shown in the figureIf the magnitudes of Q_{2} are equal, what must be the magnitude of Q_{3} in order that the net force on Q_{1} must be zero? Q_{1i} Q_{1} - Q_{2} Q_{3}? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Three point charges Q_{1} , - Q_{2} and Q_{3} are equally spaced along a line as shown in the figureIf the magnitudes of Q_{2} are equal, what must be the magnitude of Q_{3} in order that the net force on Q_{1} must be zero? Q_{1i} Q_{1} - Q_{2} Q_{3}? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three point charges Q_{1} , - Q_{2} and Q_{3} are equally spaced along a line as shown in the figureIf the magnitudes of Q_{2} are equal, what must be the magnitude of Q_{3} in order that the net force on Q_{1} must be zero? Q_{1i} Q_{1} - Q_{2} Q_{3}?.
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