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A conductor of radius r is having cavity of radius 3 are upon 4 touching the surface of the conductor with centres C1 and c2s shown to equal point charges are placed at C2 and PP is a distance of 2 are from C1 charge q is given to surface of conductor as well?
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A conductor of radius r is having cavity of radius 3 are upon 4 touchi...
Introduction
In this scenario, we have a conductor with a radius \( r \) containing a spherical cavity of radius \( \frac{3r}{4} \). The centers of the cavity and the conductor are denoted as \( C_1 \) and \( C_2 \), respectively. Two equal point charges are placed at \( C_2 \).
Charge Distribution
- The total charge \( q \) is distributed uniformly on the surface of the conductor.
- The presence of point charges induces a charge distribution on the inner surface of the cavity.
- By electrostatic shielding, the electric field inside the conductor remains zero.
Induced Charges
- The equal point charges at \( C_2 \) will induce negative charges on the inner surface of the cavity.
- The total induced charge on the inner surface will equal the sum of the point charges but of opposite sign.
Electric Field Considerations
- The electric field inside the conductor (between surface and cavity) is zero due to electrostatic shielding.
- The electric field outside the conductor behaves as if all the charge \( q \) were concentrated at the center.
Potential and Equipotential Surface
- The conductor acts as an equipotential surface, meaning every point on its surface is at the same electric potential.
- The potential inside the cavity remains uniform despite the presence of the charges, as the conductor redistributes its surface charge to maintain equilibrium.
Conclusion
This configuration illustrates fundamental principles of electrostatics, including charge distribution, electric fields, and shielding effects. Understanding these concepts is crucial for tackling advanced problems in electrostatics, particularly in the UPSC examination context.
In this scenario, we have a conductor with a radius \( r \) containing a spherical cavity of radius \( \frac{3r}{4} \). The centers of the cavity and the conductor are denoted as \( C_1 \) and \( C_2 \), respectively. Two equal point charges are placed at \( C_2 \).
Charge Distribution
- The total charge \( q \) is distributed uniformly on the surface of the conductor.
- The presence of point charges induces a charge distribution on the inner surface of the cavity.
- By electrostatic shielding, the electric field inside the conductor remains zero.
Induced Charges
- The equal point charges at \( C_2 \) will induce negative charges on the inner surface of the cavity.
- The total induced charge on the inner surface will equal the sum of the point charges but of opposite sign.
Electric Field Considerations
- The electric field inside the conductor (between surface and cavity) is zero due to electrostatic shielding.
- The electric field outside the conductor behaves as if all the charge \( q \) were concentrated at the center.
Potential and Equipotential Surface
- The conductor acts as an equipotential surface, meaning every point on its surface is at the same electric potential.
- The potential inside the cavity remains uniform despite the presence of the charges, as the conductor redistributes its surface charge to maintain equilibrium.
Conclusion
This configuration illustrates fundamental principles of electrostatics, including charge distribution, electric fields, and shielding effects. Understanding these concepts is crucial for tackling advanced problems in electrostatics, particularly in the UPSC examination context.
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A conductor of radius r is having cavity of radius 3 are upon 4 touching the surface of the conductor with centres C1 and c2s shown to equal point charges are placed at C2 and PP is a distance of 2 are from C1 charge q is given to surface of conductor as well?
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A conductor of radius r is having cavity of radius 3 are upon 4 touching the surface of the conductor with centres C1 and c2s shown to equal point charges are placed at C2 and PP is a distance of 2 are from C1 charge q is given to surface of conductor as well? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A conductor of radius r is having cavity of radius 3 are upon 4 touching the surface of the conductor with centres C1 and c2s shown to equal point charges are placed at C2 and PP is a distance of 2 are from C1 charge q is given to surface of conductor as well? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conductor of radius r is having cavity of radius 3 are upon 4 touching the surface of the conductor with centres C1 and c2s shown to equal point charges are placed at C2 and PP is a distance of 2 are from C1 charge q is given to surface of conductor as well?.
A conductor of radius r is having cavity of radius 3 are upon 4 touching the surface of the conductor with centres C1 and c2s shown to equal point charges are placed at C2 and PP is a distance of 2 are from C1 charge q is given to surface of conductor as well? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A conductor of radius r is having cavity of radius 3 are upon 4 touching the surface of the conductor with centres C1 and c2s shown to equal point charges are placed at C2 and PP is a distance of 2 are from C1 charge q is given to surface of conductor as well? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conductor of radius r is having cavity of radius 3 are upon 4 touching the surface of the conductor with centres C1 and c2s shown to equal point charges are placed at C2 and PP is a distance of 2 are from C1 charge q is given to surface of conductor as well?.
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