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A spherical shell of radius r is given charge 3q on its surfaca and a point charge 2q is placed outside the shell at a distance of 2r from centre ,now find potential at centre?
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A spherical shell of radius r is given charge 3q on its surfaca and a ...
Problem: Find the potential at the center of a spherical shell of radius r given charge 3q on its surface and a point charge 2q placed outside the shell at a distance of 2r from the center.
Solution:
Step 1: Identify the relevant formulas
To solve this problem, we need to use the formula for the potential due to a point charge and the potential due to a spherical shell.
The potential V at a point P due to a point charge q located at a distance r from P is given by:
V = kq / r
Where k is the Coulomb constant and its value is 1 / 4πε0.
The potential at a point inside or outside a spherical shell of radius R carrying a charge Q is given by:
V = kQ / R
Step 2: Calculate the potential due to the point charge
The point charge 2q is placed outside the shell at a distance of 2r from the center. Therefore, the potential at the center due to this point charge is:
V1 = k(2q) / (2r) = kq / r
Step 3: Calculate the potential due to the spherical shell
The spherical shell has a charge of 3q distributed uniformly on its surface. Therefore, the potential at the center due to the spherical shell is:
V2 = k(3q) / r = 3kq / r
Step 4: Calculate the total potential at the center
The total potential at the center due to both the point charge and the spherical shell is the sum of the potentials due to each of them.
V = V1 + V2 = kq / r + 3kq / r = 4kq / r
Substituting the value of k, we get:
V = q / (4πε0r)
Therefore, the potential at the center is q / (4πε0r).
Conclusion: The potential at the center of the spherical shell is q / (4πε0r).
Solution:
Step 1: Identify the relevant formulas
To solve this problem, we need to use the formula for the potential due to a point charge and the potential due to a spherical shell.
The potential V at a point P due to a point charge q located at a distance r from P is given by:
V = kq / r
Where k is the Coulomb constant and its value is 1 / 4πε0.
The potential at a point inside or outside a spherical shell of radius R carrying a charge Q is given by:
V = kQ / R
Step 2: Calculate the potential due to the point charge
The point charge 2q is placed outside the shell at a distance of 2r from the center. Therefore, the potential at the center due to this point charge is:
V1 = k(2q) / (2r) = kq / r
Step 3: Calculate the potential due to the spherical shell
The spherical shell has a charge of 3q distributed uniformly on its surface. Therefore, the potential at the center due to the spherical shell is:
V2 = k(3q) / r = 3kq / r
Step 4: Calculate the total potential at the center
The total potential at the center due to both the point charge and the spherical shell is the sum of the potentials due to each of them.
V = V1 + V2 = kq / r + 3kq / r = 4kq / r
Substituting the value of k, we get:
V = q / (4πε0r)
Therefore, the potential at the center is q / (4πε0r).
Conclusion: The potential at the center of the spherical shell is q / (4πε0r).
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A spherical shell of radius r is given charge 3q on its surfaca and a point charge 2q is placed outside the shell at a distance of 2r from centre ,now find potential at centre?
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A spherical shell of radius r is given charge 3q on its surfaca and a point charge 2q is placed outside the shell at a distance of 2r from centre ,now find potential at centre? 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 A spherical shell of radius r is given charge 3q on its surfaca and a point charge 2q is placed outside the shell at a distance of 2r from centre ,now find potential at centre? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical shell of radius r is given charge 3q on its surfaca and a point charge 2q is placed outside the shell at a distance of 2r from centre ,now find potential at centre?.
A spherical shell of radius r is given charge 3q on its surfaca and a point charge 2q is placed outside the shell at a distance of 2r from centre ,now find potential at centre? 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 A spherical shell of radius r is given charge 3q on its surfaca and a point charge 2q is placed outside the shell at a distance of 2r from centre ,now find potential at centre? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical shell of radius r is given charge 3q on its surfaca and a point charge 2q is placed outside the shell at a distance of 2r from centre ,now find potential at centre?.
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