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Two similar spheres when placed 2cm. apart attract each other with a force of 4dynes. The spheres are connected by a wire on removing the wire the spheres now repel each other with a force of 2.5dynes. Calculate the initial charges on the sphere neglecting the capacity of wire?
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Two similar spheres when placed 2cm. apart attract each other with a f...
Calculation of Initial Charges on Spheres
Given that two similar spheres placed 2cm apart attract each other with a force of 4dynes and repel each other with a force of 2.5dynes when the wire connecting them is removed. We need to calculate the initial charges on the spheres.
Understanding Coulomb's Law
Coulomb's law states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, Coulomb's law is represented as:
F = K*q1*q2/d^2
Where F is the force of attraction or repulsion, q1 and q2 are the charges on the two objects, d is the distance between them, and K is the Coulomb's constant.
Calculating the Charges
We can use the given information to calculate the charges on the spheres as follows:
- When the spheres attract each other with a force of 4dynes, the charges on the spheres are of opposite signs.
- Let the charges on the spheres be q and -q.
- Using Coulomb's law, we can write:
- When the wire is removed, the spheres repel each other with a force of 2.5dynes, which means that the charges on the spheres are of the same sign.
- Let the charges on the spheres be q and q.
- Using Coulomb's law, we can write:
4 = K*q*(-q)/0.02^2
4 = K*q^2/0.0004
q^2 = 4*0.0004/K
q = sqrt(4*0.0004/K)
2.5 = K*q*q/0.02^2
q^2 = 2.5*0.0004/K
q = sqrt(2.5*0.0004/K)
Substituting Values
Now, we need to substitute the value of K in the above equations.
K = 1/4*pi*epsilon, where epsilon is the permittivity of free space.
Substituting the value of epsilon, we get:
K = 9*10^9 N-m^2/C^2
Substituting this value in the above equations, we get:
- q = 2*10^-6 C when the spheres attract each other.
- q = 1.58*10^-6 C when the wire is removed and the spheres repel each other.
Conclusion
Therefore, the initial charges on the spheres are 2*10^-
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Two similar spheres when placed 2cm. apart attract each other with a force of 4dynes. The spheres are connected by a wire on removing the wire the spheres now repel each other with a force of 2.5dynes. Calculate the initial charges on the sphere neglecting the capacity of wire?
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Two similar spheres when placed 2cm. apart attract each other with a force of 4dynes. The spheres are connected by a wire on removing the wire the spheres now repel each other with a force of 2.5dynes. Calculate the initial charges on the sphere neglecting the capacity of wire? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two similar spheres when placed 2cm. apart attract each other with a force of 4dynes. The spheres are connected by a wire on removing the wire the spheres now repel each other with a force of 2.5dynes. Calculate the initial charges on the sphere neglecting the capacity of wire? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two similar spheres when placed 2cm. apart attract each other with a force of 4dynes. The spheres are connected by a wire on removing the wire the spheres now repel each other with a force of 2.5dynes. Calculate the initial charges on the sphere neglecting the capacity of wire?.
Two similar spheres when placed 2cm. apart attract each other with a force of 4dynes. The spheres are connected by a wire on removing the wire the spheres now repel each other with a force of 2.5dynes. Calculate the initial charges on the sphere neglecting the capacity of wire? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two similar spheres when placed 2cm. apart attract each other with a force of 4dynes. The spheres are connected by a wire on removing the wire the spheres now repel each other with a force of 2.5dynes. Calculate the initial charges on the sphere neglecting the capacity of wire? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two similar spheres when placed 2cm. apart attract each other with a force of 4dynes. The spheres are connected by a wire on removing the wire the spheres now repel each other with a force of 2.5dynes. Calculate the initial charges on the sphere neglecting the capacity of wire?.
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