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Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and C
- a)F/4
- b)3F/4
- c)F/8
- d)3F/8
Correct answer is option 'D'. Can you explain this answer?
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Two spherical conductors B and C having equal radii and carrying equal...
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Two spherical conductors B and C having equal radii and carrying equal...
Explanation:
When two conductors carrying equal charges repel each other with a force F, it means that the force of repulsion is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Let the charges on conductors B and C be q.
Step 1: Bringing the third conductor in contact with B
When the uncharged conductor is brought in contact with conductor B, some of the charge on B will be transferred to the uncharged conductor due to the process of conduction. Let the charge transferred be q1.
After the transfer of charge, conductor B will have a charge of q-q1 and the uncharged conductor will have a charge of q1.
Step 2: Bringing the third conductor in contact with C
Now, when the third conductor (charged with q1) is brought in contact with conductor C, some charge will be transferred from the conductor to C. Let the charge transferred be q2.
After the transfer of charge, conductor C will have a charge of q+q2 and the uncharged conductor will have a charge of q1-q2.
Step 3: Removing the third conductor
After the transfer of charge from B to C, the uncharged conductor is removed from both B and C. Now, conductor B will have a charge of q-q1 and conductor C will have a charge of q+q2.
Calculating the new force of repulsion between B and C
The new force of repulsion between B and C can be calculated using the formula:
F' = k * [(q-q1) * (q+q2)] / d^2
where k is the electrostatic constant and d is the distance between B and C.
Now, to simplify the expression, we can expand and rearrange the terms:
F' = k * [(q^2 - q1^2) + q*q2 - q1*q2] / d^2
Since q1 is the charge transferred from B to the uncharged conductor, and q2 is the charge transferred from the uncharged conductor to C, we can write:
q1 = q - q'
q2 = q' - q''
where q' is the final charge on the uncharged conductor after the transfer of charge from B to C, and q'' is the charge remaining on the uncharged conductor after the second transfer.
Substituting the values of q1 and q2 in the expression for F', we get:
F' = k * [(q^2 - (q - q')^2) + q*(q' - q'') - (q - q')*(q' - q'')] / d^2
Simplifying the expression further:
F' = k * [(q^2 - (q^2 - 2*q*q' + q'^2)) + q*q' - q*q'' - (q*q' - q*q'') + (q - q')*(q' - q'')] / d^2
F' = k * [2*q*q' - 2*q*q'' + (q - q')*(q' - q'')] / d^2
Since q' and q'' are very small compared to q, we can neglect their squares and higher powers. Thus,
When two conductors carrying equal charges repel each other with a force F, it means that the force of repulsion is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Let the charges on conductors B and C be q.
Step 1: Bringing the third conductor in contact with B
When the uncharged conductor is brought in contact with conductor B, some of the charge on B will be transferred to the uncharged conductor due to the process of conduction. Let the charge transferred be q1.
After the transfer of charge, conductor B will have a charge of q-q1 and the uncharged conductor will have a charge of q1.
Step 2: Bringing the third conductor in contact with C
Now, when the third conductor (charged with q1) is brought in contact with conductor C, some charge will be transferred from the conductor to C. Let the charge transferred be q2.
After the transfer of charge, conductor C will have a charge of q+q2 and the uncharged conductor will have a charge of q1-q2.
Step 3: Removing the third conductor
After the transfer of charge from B to C, the uncharged conductor is removed from both B and C. Now, conductor B will have a charge of q-q1 and conductor C will have a charge of q+q2.
Calculating the new force of repulsion between B and C
The new force of repulsion between B and C can be calculated using the formula:
F' = k * [(q-q1) * (q+q2)] / d^2
where k is the electrostatic constant and d is the distance between B and C.
Now, to simplify the expression, we can expand and rearrange the terms:
F' = k * [(q^2 - q1^2) + q*q2 - q1*q2] / d^2
Since q1 is the charge transferred from B to the uncharged conductor, and q2 is the charge transferred from the uncharged conductor to C, we can write:
q1 = q - q'
q2 = q' - q''
where q' is the final charge on the uncharged conductor after the transfer of charge from B to C, and q'' is the charge remaining on the uncharged conductor after the second transfer.
Substituting the values of q1 and q2 in the expression for F', we get:
F' = k * [(q^2 - (q - q')^2) + q*(q' - q'') - (q - q')*(q' - q'')] / d^2
Simplifying the expression further:
F' = k * [(q^2 - (q^2 - 2*q*q' + q'^2)) + q*q' - q*q'' - (q*q' - q*q'') + (q - q')*(q' - q'')] / d^2
F' = k * [2*q*q' - 2*q*q'' + (q - q')*(q' - q'')] / d^2
Since q' and q'' are very small compared to q, we can neglect their squares and higher powers. Thus,
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Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and Ca)F/4b)3F/4c)F/8d)3F/8Correct answer is option 'D'. Can you explain this answer?
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Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and Ca)F/4b)3F/4c)F/8d)3F/8Correct answer is option 'D'. Can you explain this answer? 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 Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and Ca)F/4b)3F/4c)F/8d)3F/8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and Ca)F/4b)3F/4c)F/8d)3F/8Correct answer is option 'D'. Can you explain this answer?.
Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and Ca)F/4b)3F/4c)F/8d)3F/8Correct answer is option 'D'. Can you explain this answer? 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 Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and Ca)F/4b)3F/4c)F/8d)3F/8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and Ca)F/4b)3F/4c)F/8d)3F/8Correct answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice Two spherical conductors B and C having equal radii and carrying equal charges repel each other witha force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed awayfrom both. The new force of repulsion between B and Ca)F/4b)3F/4c)F/8d)3F/8Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 12 tests.
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