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A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant then
- a)The electrostatic energy will decrease by a factor 3
- b)The electrostatic energy will decrease by a factor 1.5
- c)The electrostatic energy will increase by a factor 3
- d)The electrostatic energy will be increase by a factor 1.5
Correct answer is option 'D'. Can you explain this answer?
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A phserical shell of radius R and carrying charge Q. Now, if we decrea...
The electrostatic energy of the given charge distribution is
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A phserical shell of radius R and carrying charge Q. Now, if we decrea...
Explanation:
To understand why the electrostatic energy will increase by a factor of 1.5 when the radius of the spherical shell is decreased by (R/3) while keeping the charge constant, we need to analyze the relationship between electrostatic energy and the radius of a charged sphere.
1. Electrostatic Energy:
The electrostatic energy of a charged sphere is given by the formula:
E = (3/5) * (k * Q^2) / R
where E is the electrostatic energy, k is the electrostatic constant, Q is the charge on the sphere, and R is the radius of the sphere.
2. Decreasing the Radius:
Now, let's consider the scenario where the radius of the spherical shell is decreased by (R/3) while keeping the charge constant. This means the new radius of the shell will be (2R/3).
3. Calculating the New Electrostatic Energy:
Using the formula for electrostatic energy, we can calculate the new electrostatic energy:
E' = (3/5) * (k * Q^2) / (2R/3)
Simplifying the expression:
E' = (9/10) * (k * Q^2) / R
4. Comparing the Original and New Energy:
To determine the factor by which the electrostatic energy changes, we can calculate the ratio of the new energy (E') to the original energy (E):
E' / E = [(9/10) * (k * Q^2) / R] / [(3/5) * (k * Q^2) / R]
Simplifying the expression:
E' / E = (9/10) / (3/5) = (9/10) * (5/3) = 3/2 = 1.5
Therefore, the electrostatic energy will increase by a factor of 1.5 when the radius of the spherical shell is decreased by (R/3) while keeping the charge constant.
Conclusion:
The correct answer is option 'D': The electrostatic energy will increase by a factor of 1.5.
To understand why the electrostatic energy will increase by a factor of 1.5 when the radius of the spherical shell is decreased by (R/3) while keeping the charge constant, we need to analyze the relationship between electrostatic energy and the radius of a charged sphere.
1. Electrostatic Energy:
The electrostatic energy of a charged sphere is given by the formula:
E = (3/5) * (k * Q^2) / R
where E is the electrostatic energy, k is the electrostatic constant, Q is the charge on the sphere, and R is the radius of the sphere.
2. Decreasing the Radius:
Now, let's consider the scenario where the radius of the spherical shell is decreased by (R/3) while keeping the charge constant. This means the new radius of the shell will be (2R/3).
3. Calculating the New Electrostatic Energy:
Using the formula for electrostatic energy, we can calculate the new electrostatic energy:
E' = (3/5) * (k * Q^2) / (2R/3)
Simplifying the expression:
E' = (9/10) * (k * Q^2) / R
4. Comparing the Original and New Energy:
To determine the factor by which the electrostatic energy changes, we can calculate the ratio of the new energy (E') to the original energy (E):
E' / E = [(9/10) * (k * Q^2) / R] / [(3/5) * (k * Q^2) / R]
Simplifying the expression:
E' / E = (9/10) / (3/5) = (9/10) * (5/3) = 3/2 = 1.5
Therefore, the electrostatic energy will increase by a factor of 1.5 when the radius of the spherical shell is decreased by (R/3) while keeping the charge constant.
Conclusion:
The correct answer is option 'D': The electrostatic energy will increase by a factor of 1.5.
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A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer?
Question Description
A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer?.
A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer?.
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A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A phserical shell of radius R and carrying charge Q. Now, if we decrease radius by (R/3) keeping the charge constant thena)The electrostatic energy will decrease by a factor 3b)The electrostatic energy will decrease by a factor 1.5c)The electrostatic energy will increase by a factor 3d)The electrostatic energywill be increase by a factor 1.5Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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