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A small charged spherical shell of radius 0.01 m is at a potential of 30 V. The electrostatic energy of the shell is
- a)10-10 J
- b)5 x 10-10 J
- c)5 x 10-9 J
- d)10-9 J
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A small charged spherical shell of radius 0.01 m is at a potential of ...
Given information:
- Radius of the charged spherical shell, r = 0.01 m
- Potential of the shell, V = 30 V
Formula:
The electrostatic energy of a charged spherical shell is given by the formula:
E = (Q^2) / (8πε₀r)
where Q is the charge on the shell, ε₀ is the permittivity of free space, and r is the radius of the shell.
Explanation:
To find the electrostatic energy of the shell, we need to determine the charge on the shell, Q. Since the problem statement does not provide the charge explicitly, we need to find it using the potential.
Finding the charge:
The potential of a charged spherical shell is given by the formula:
V = (Q / (4πε₀r))
Rearranging the formula, we can find the charge Q:
Q = V * (4πε₀r)
Substituting the given values:
Q = 30 V * (4πε₀ * 0.01 m)
Calculating the charge:
The permittivity of free space, ε₀, has a value of approximately 8.854 x 10^-12 F/m.
Substituting the value of ε₀ in the equation:
Q = 30 V * (4π * 8.854 x 10^-12 F/m * 0.01 m)
Simplifying the equation:
Q = 30 V * (4π * 8.854 x 10^-14 F)
Calculating the electrostatic energy:
Now that we have the charge on the shell, we can calculate the electrostatic energy using the formula:
E = (Q^2) / (8πε₀r)
Substituting the values:
E = (Q^2) / (8πε₀r)
= (Q^2) / (8π * 8.854 x 10^-12 F/m * 0.01 m)
Simplifying the equation:
E = (Q^2) / (8π * 8.854 x 10^-14 F)
= (Q^2) / (70.72 x 10^-14 F)
= (Q^2) / (7.072 x 10^-12 F)
Substituting the value of Q:
E = (30 V * (4π * 8.854 x 10^-14 F))^2 / (7.072 x 10^-12 F)
Simplifying the equation:
E = (30 * 4π * 8.854 x 10^-14 F)^2 / (7.072 x 10^-12 F)
= (30 * 4π * 8.854 x 10^-14 F)^2 / (7.072 x 10^-12 F)
≈ 5 x 10^-10 J
Therefore, the electrostatic energy of the charged spherical shell is approximately 5 x 10^-10 J, which corresponds to option B.
- Radius of the charged spherical shell, r = 0.01 m
- Potential of the shell, V = 30 V
Formula:
The electrostatic energy of a charged spherical shell is given by the formula:
E = (Q^2) / (8πε₀r)
where Q is the charge on the shell, ε₀ is the permittivity of free space, and r is the radius of the shell.
Explanation:
To find the electrostatic energy of the shell, we need to determine the charge on the shell, Q. Since the problem statement does not provide the charge explicitly, we need to find it using the potential.
Finding the charge:
The potential of a charged spherical shell is given by the formula:
V = (Q / (4πε₀r))
Rearranging the formula, we can find the charge Q:
Q = V * (4πε₀r)
Substituting the given values:
Q = 30 V * (4πε₀ * 0.01 m)
Calculating the charge:
The permittivity of free space, ε₀, has a value of approximately 8.854 x 10^-12 F/m.
Substituting the value of ε₀ in the equation:
Q = 30 V * (4π * 8.854 x 10^-12 F/m * 0.01 m)
Simplifying the equation:
Q = 30 V * (4π * 8.854 x 10^-14 F)
Calculating the electrostatic energy:
Now that we have the charge on the shell, we can calculate the electrostatic energy using the formula:
E = (Q^2) / (8πε₀r)
Substituting the values:
E = (Q^2) / (8πε₀r)
= (Q^2) / (8π * 8.854 x 10^-12 F/m * 0.01 m)
Simplifying the equation:
E = (Q^2) / (8π * 8.854 x 10^-14 F)
= (Q^2) / (70.72 x 10^-14 F)
= (Q^2) / (7.072 x 10^-12 F)
Substituting the value of Q:
E = (30 V * (4π * 8.854 x 10^-14 F))^2 / (7.072 x 10^-12 F)
Simplifying the equation:
E = (30 * 4π * 8.854 x 10^-14 F)^2 / (7.072 x 10^-12 F)
= (30 * 4π * 8.854 x 10^-14 F)^2 / (7.072 x 10^-12 F)
≈ 5 x 10^-10 J
Therefore, the electrostatic energy of the charged spherical shell is approximately 5 x 10^-10 J, which corresponds to option B.
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A small charged spherical shell of radius 0.01 m is at a potential of ...
Energy =(q^2)/(8π£R)
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A small charged spherical shell of radius 0.01 m is at a potential of 30 V. The electrostatic energy of the shell isa)10-10 Jb)5 x 10-10 Jc)5 x 10-9 Jd)10-9 JCorrect answer is option 'B'. Can you explain this answer?
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