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Two spheres A and B of radius a and b respectively are at same electric potential. The ratio of the surface charge densities of A and B is .?
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Two spheres A and B of radius a and b respectively are at same electri...
Explanation:
When two conducting spheres A and B of radius a and b respectively are at the same electric potential, the ratio of surface charge densities of A and B can be found using the following formula:
Formula:
Surface charge density = Q / A
where Q is the charge on the sphere and A is the surface area of the sphere.
Calculation:
Let the charge on sphere A be Qa and the charge on sphere B be Qb.
Since both the spheres are at the same potential, the potential difference between them is zero.
Hence, we have:
Va - Vb = 0
or
(kQa / a) - (kQb / b) = 0
where k is the Coulomb's constant.
Solving for Qa / Qb, we get:
Qa / Qb = (a / b)
Now, using the formula for surface charge density, we have:
Surface charge density of A = Qa / (4πa²)
Surface charge density of B = Qb / (4πb²)
Substituting the value of Qa / Qb, we get:
Surface charge density of A / Surface charge density of B = (Qa / (4πa²)) / (Qb / (4πb²))
= (a / b) * (b² / a²)
= b / a
Hence, the ratio of surface charge densities of A and B is b / a.
Conclusion:
The ratio of surface charge densities of two spheres A and B of radii a and b respectively, when they are at the same electric potential, is given by b / a.
When two conducting spheres A and B of radius a and b respectively are at the same electric potential, the ratio of surface charge densities of A and B can be found using the following formula:
Formula:
Surface charge density = Q / A
where Q is the charge on the sphere and A is the surface area of the sphere.
Calculation:
Let the charge on sphere A be Qa and the charge on sphere B be Qb.
Since both the spheres are at the same potential, the potential difference between them is zero.
Hence, we have:
Va - Vb = 0
or
(kQa / a) - (kQb / b) = 0
where k is the Coulomb's constant.
Solving for Qa / Qb, we get:
Qa / Qb = (a / b)
Now, using the formula for surface charge density, we have:
Surface charge density of A = Qa / (4πa²)
Surface charge density of B = Qb / (4πb²)
Substituting the value of Qa / Qb, we get:
Surface charge density of A / Surface charge density of B = (Qa / (4πa²)) / (Qb / (4πb²))
= (a / b) * (b² / a²)
= b / a
Hence, the ratio of surface charge densities of A and B is b / a.
Conclusion:
The ratio of surface charge densities of two spheres A and B of radii a and b respectively, when they are at the same electric potential, is given by b / a.
Community Answer
Two spheres A and B of radius a and b respectively are at same electri...
Ratio is b/a.
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Two spheres A and B of radius a and b respectively are at same electric potential. The ratio of the surface charge densities of A and B is .?
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Two spheres A and B of radius a and b respectively are at same electric potential. The ratio of the surface charge densities of A and B is .? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two spheres A and B of radius a and b respectively are at same electric potential. The ratio of the surface charge densities of A and B is .? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spheres A and B of radius a and b respectively are at same electric potential. The ratio of the surface charge densities of A and B is .?.
Two spheres A and B of radius a and b respectively are at same electric potential. The ratio of the surface charge densities of A and B is .? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two spheres A and B of radius a and b respectively are at same electric potential. The ratio of the surface charge densities of A and B is .? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spheres A and B of radius a and b respectively are at same electric potential. The ratio of the surface charge densities of A and B is .?.
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