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Three point charges Q, 2Q and -3Q are placed at the vertices of an equilateral triangle ABC of side l . If these charges are displaced to their midpoints A1,B1and C1 respectively , find the amount of work done in shifting the charges to their new location?
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Three point charges Q, 2Q and -3Q are placed at the vertices of an eq...
**Solution:**
To find the amount of work done in shifting the charges to their new location, we need to calculate the work done for each charge individually and then add them up.
Let's consider the charge Q at vertex A. When it is displaced to its midpoint A1, the distance it moves is half of the side length of the equilateral triangle (l/2). The force experienced by charge Q due to the other two charges can be calculated using Coulomb's law:
F = k * (Q * 2Q) / (l/2)^2
where k is the electrostatic constant.
The work done in moving charge Q from A to A1 is given by:
W1 = F * (l/2)
Similarly, for charge 2Q at vertex B, the force experienced due to the other two charges is:
F = k * (2Q * -3Q) / (l/2)^2
The work done in moving charge 2Q from B to B1 is:
W2 = F * (l/2)
Finally, for charge -3Q at vertex C, the force experienced due to the other two charges is:
F = k * (-3Q * Q) / (l/2)^2
The work done in moving charge -3Q from C to C1 is:
W3 = F * (l/2)
Now, we can calculate the total work done by adding up the individual work done for each charge:
Total work done = W1 + W2 + W3
Let's simplify the expression:
Total work done = (F * (l/2)) + (F * (l/2)) + (F * (l/2))
Total work done = F * l
Substituting the expression for force F:
Total work done = k * (Q * 2Q) / (l/2)^2 * l
Total work done = k * Q * 2Q * 4 / l * l
Total work done = 8kQ^2 / l
Therefore, the amount of work done in shifting the charges to their new location is 8kQ^2 / l.
To find the amount of work done in shifting the charges to their new location, we need to calculate the work done for each charge individually and then add them up.
Let's consider the charge Q at vertex A. When it is displaced to its midpoint A1, the distance it moves is half of the side length of the equilateral triangle (l/2). The force experienced by charge Q due to the other two charges can be calculated using Coulomb's law:
F = k * (Q * 2Q) / (l/2)^2
where k is the electrostatic constant.
The work done in moving charge Q from A to A1 is given by:
W1 = F * (l/2)
Similarly, for charge 2Q at vertex B, the force experienced due to the other two charges is:
F = k * (2Q * -3Q) / (l/2)^2
The work done in moving charge 2Q from B to B1 is:
W2 = F * (l/2)
Finally, for charge -3Q at vertex C, the force experienced due to the other two charges is:
F = k * (-3Q * Q) / (l/2)^2
The work done in moving charge -3Q from C to C1 is:
W3 = F * (l/2)
Now, we can calculate the total work done by adding up the individual work done for each charge:
Total work done = W1 + W2 + W3
Let's simplify the expression:
Total work done = (F * (l/2)) + (F * (l/2)) + (F * (l/2))
Total work done = F * l
Substituting the expression for force F:
Total work done = k * (Q * 2Q) / (l/2)^2 * l
Total work done = k * Q * 2Q * 4 / l * l
Total work done = 8kQ^2 / l
Therefore, the amount of work done in shifting the charges to their new location is 8kQ^2 / l.
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Three point charges Q, 2Q and -3Q are placed at the vertices of an equilateral triangle ABC of side l . If these charges are displaced to their midpoints A1,B1and C1 respectively , find the amount of work done in shifting the charges to their new location?
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Three point charges Q, 2Q and -3Q are placed at the vertices of an equilateral triangle ABC of side l . If these charges are displaced to their midpoints A1,B1and C1 respectively , find the amount of work done in shifting the charges to their new location? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Three point charges Q, 2Q and -3Q are placed at the vertices of an equilateral triangle ABC of side l . If these charges are displaced to their midpoints A1,B1and C1 respectively , find the amount of work done in shifting the charges to their new location? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three point charges Q, 2Q and -3Q are placed at the vertices of an equilateral triangle ABC of side l . If these charges are displaced to their midpoints A1,B1and C1 respectively , find the amount of work done in shifting the charges to their new location?.
Three point charges Q, 2Q and -3Q are placed at the vertices of an equilateral triangle ABC of side l . If these charges are displaced to their midpoints A1,B1and C1 respectively , find the amount of work done in shifting the charges to their new location? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Three point charges Q, 2Q and -3Q are placed at the vertices of an equilateral triangle ABC of side l . If these charges are displaced to their midpoints A1,B1and C1 respectively , find the amount of work done in shifting the charges to their new location? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three point charges Q, 2Q and -3Q are placed at the vertices of an equilateral triangle ABC of side l . If these charges are displaced to their midpoints A1,B1and C1 respectively , find the amount of work done in shifting the charges to their new location?.
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