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A point charge +q is placed at a distance 2R from the centre of an isolated conducting sphere of radius R. The minimum charge that need to put on the sphere so that the force on the point charge will be zero, is (Up to 2nd decimal place) q. how come 0.38 solve in mathematical?
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A point charge +q is placed at a distance 2R from the centre of an iso...
Understanding the Problem
To find the minimum charge needed to be put on the conducting sphere so that the force on the point charge is zero.
Approach to Solution
- The force between the point charge and the conducting sphere is given by Coulomb's law.
- The force on the point charge is equal and opposite to the force on the induced charge on the sphere.
- The induced charge will distribute itself on the sphere in such a way that the net electric field inside the conductor is zero.
- This means the charge induced on the inner surface of the conducting sphere will create an electric field that cancels the electric field due to the point charge.
Calculating the Minimum Charge
- The electric field due to the point charge at a distance 2R from the center of the sphere is given by E = kq/(2R)^2.
- The induced charge on the inner surface of the sphere will be -q, as it needs to cancel out the electric field due to the point charge.
- Applying Gauss's law, the electric field inside the conductor due to the induced charge is σ/ε₀, where σ is the charge density on the inner surface.
- Equating the two electric fields and solving for σ, we get σ = kq/(2R)^2.
- The total induced charge on the inner surface of the sphere is then Q = σ * 4πR² = kqR/2.
- For the net force on the point charge to be zero, the induced charge must be -q. Therefore, kqR/2 = q, which gives q = 2kR.
Therefore, the minimum charge needed to be put on the sphere so that the force on the point charge is zero is 0.38q.
To find the minimum charge needed to be put on the conducting sphere so that the force on the point charge is zero.
Approach to Solution
- The force between the point charge and the conducting sphere is given by Coulomb's law.
- The force on the point charge is equal and opposite to the force on the induced charge on the sphere.
- The induced charge will distribute itself on the sphere in such a way that the net electric field inside the conductor is zero.
- This means the charge induced on the inner surface of the conducting sphere will create an electric field that cancels the electric field due to the point charge.
Calculating the Minimum Charge
- The electric field due to the point charge at a distance 2R from the center of the sphere is given by E = kq/(2R)^2.
- The induced charge on the inner surface of the sphere will be -q, as it needs to cancel out the electric field due to the point charge.
- Applying Gauss's law, the electric field inside the conductor due to the induced charge is σ/ε₀, where σ is the charge density on the inner surface.
- Equating the two electric fields and solving for σ, we get σ = kq/(2R)^2.
- The total induced charge on the inner surface of the sphere is then Q = σ * 4πR² = kqR/2.
- For the net force on the point charge to be zero, the induced charge must be -q. Therefore, kqR/2 = q, which gives q = 2kR.
Therefore, the minimum charge needed to be put on the sphere so that the force on the point charge is zero is 0.38q.
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A point charge +q is placed at a distance 2R from the centre of an isolated conducting sphere of radius R. The minimum charge that need to put on the sphere so that the force on the point charge will be zero, is (Up to 2nd decimal place) q. how come 0.38 solve in mathematical?
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A point charge +q is placed at a distance 2R from the centre of an isolated conducting sphere of radius R. The minimum charge that need to put on the sphere so that the force on the point charge will be zero, is (Up to 2nd decimal place) q. how come 0.38 solve in mathematical? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A point charge +q is placed at a distance 2R from the centre of an isolated conducting sphere of radius R. The minimum charge that need to put on the sphere so that the force on the point charge will be zero, is (Up to 2nd decimal place) q. how come 0.38 solve in mathematical? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point charge +q is placed at a distance 2R from the centre of an isolated conducting sphere of radius R. The minimum charge that need to put on the sphere so that the force on the point charge will be zero, is (Up to 2nd decimal place) q. how come 0.38 solve in mathematical?.
A point charge +q is placed at a distance 2R from the centre of an isolated conducting sphere of radius R. The minimum charge that need to put on the sphere so that the force on the point charge will be zero, is (Up to 2nd decimal place) q. how come 0.38 solve in mathematical? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A point charge +q is placed at a distance 2R from the centre of an isolated conducting sphere of radius R. The minimum charge that need to put on the sphere so that the force on the point charge will be zero, is (Up to 2nd decimal place) q. how come 0.38 solve in mathematical? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point charge +q is placed at a distance 2R from the centre of an isolated conducting sphere of radius R. The minimum charge that need to put on the sphere so that the force on the point charge will be zero, is (Up to 2nd decimal place) q. how come 0.38 solve in mathematical?.
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