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two identical spheres having charges of opposite sign are placed 3m apart attract each other with a force 2.4*10^-3N.now spheres are touched and then placed at original separation with a force 10^-3N. find initial charges on sphere?
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?two identical spheres having charges of opposite sign are placed 3m a...
Ans.
Method to Solve :
Here,
F1 = 0.108 N
r = 0.5 m
F2 = 0.036 N
Let charges on the spheres be q1 and q2 respectively.
Charges after connection gets redistributed in the spheres, so be q in each of the spheres
From conservation of charge
q1 + q2 = 2q ---1.
Again
F1 = k q1q2/r2 ---2
F2 = k q2/r2 ----3
=> 0.036 = 9�109�q2/(0.5)2
=> q2 = 0.036�(0.5)2/9�109
=> q2 = 0.036/(4�9�109)
=> q2 = 1�10-12
=> q = 1�10-6 C ---4
From 2 and 3
F1/F2 = q1q2/q2
=> 3 = q1q2/q2
=> 3q2 = q1q2
=> q1q2 = 3q2
Again,
(q1 – q2)2 = (q1 + q2)2 – 4q1q2
= (2q)2 – 3q2/ r2
= q2/ r2
By 4
(q1 – q2) = q/r
= 1�10-6/ 0.5
= 2�10-6 ---5
From 1 and 4.
q1 + q2 = 4�10-6 ---6.
Adding 5 and 6
q1 = 3�10-6
= 3μC
Subtracting 5 from 6
q2 = 1�10-6
= 1μC
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?two identical spheres having charges of opposite sign are placed 3m a...
Initial Charges on Spheres
- Let's denote the charges on the spheres as q1 and q2, where q1 is positive and q2 is negative.
Initial Force between Spheres
- The force between the spheres can be calculated using Coulomb's law: F = k * |q1 * q2| / r^2, where k is the electrostatic constant, r is the separation distance.
- Given F = 2.4 * 10^-3 N, r = 3m, k = 9 * 10^9 Nm^2/C^2.
- Substituting the values, we get 2.4 * 10^-3 = (9 * 10^9) * |q1 * q2| / 3^2.
Charging by Induction
- When the spheres are touched, they will equalize their charges due to the principle of charging by induction.
- The negative sphere will transfer some charge to the positive sphere until they both have the same charge magnitude.
Final Force between Spheres
- After touching and separating the spheres, the force between them becomes 10^-3 N.
- Using the same formula as before, 10^-3 = (9 * 10^9) * |q1 * q2| / 3^2.
- Since the spheres now have the same charge, q1 = -q2.
- Solving the two equations simultaneously, we can find the initial charges on the spheres.
Therefore, by solving the equations, we can determine the initial charges on the spheres.
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?two identical spheres having charges of opposite sign are placed 3m apart attract each other with a force 2.4*10^-3N.now spheres are touched and then placed at original separation with a force 10^-3N. find initial charges on sphere? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about ?two identical spheres having charges of opposite sign are placed 3m apart attract each other with a force 2.4*10^-3N.now spheres are touched and then placed at original separation with a force 10^-3N. find initial charges on sphere? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?two identical spheres having charges of opposite sign are placed 3m apart attract each other with a force 2.4*10^-3N.now spheres are touched and then placed at original separation with a force 10^-3N. find initial charges on sphere?.
?two identical spheres having charges of opposite sign are placed 3m apart attract each other with a force 2.4*10^-3N.now spheres are touched and then placed at original separation with a force 10^-3N. find initial charges on sphere? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about ?two identical spheres having charges of opposite sign are placed 3m apart attract each other with a force 2.4*10^-3N.now spheres are touched and then placed at original separation with a force 10^-3N. find initial charges on sphere? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?two identical spheres having charges of opposite sign are placed 3m apart attract each other with a force 2.4*10^-3N.now spheres are touched and then placed at original separation with a force 10^-3N. find initial charges on sphere?.
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