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The electric flux from a cube of side ‘a’ is ‘Φ’. What will be its value if the side of the cube is made ‘2a’ and the charge enclosed is made half?
- a)Φ/2
- b)Φ
- c)4 Φ
- d)2 Φ
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The electric flux from a cube of side ‘a’ is ‘Φ&...
Understanding Electric Flux
Electric flux is defined as the flow of electric field through a surface. According to Gauss's Law, the electric flux (Φ) through a closed surface is proportional to the charge (Q) enclosed by that surface:
Φ = Q / ε₀
where ε₀ is the permittivity of free space.
Scenario 1: Original Cube
- Consider a cube with side length 'a.'
- The electric flux through this cube is given as Φ.
- The charge enclosed in this cube is Q.
Scenario 2: Modified Cube
- The side of the cube is now doubled to '2a.'
- The volume of the cube increases, but the charge enclosed is halved (Q/2).
Applying Gauss's Law
- For the new cube, using Gauss's Law:
Φ' = Q' / ε₀
- Since the new charge Q' = Q/2, we have:
Φ' = (Q/2) / ε₀
Relating New Flux to Original Flux
- The original flux Φ was:
Φ = Q / ε₀
- Therefore, substituting Q' into the equation for the new electric flux:
Φ' = (1/2) * (Q / ε₀) = (1/2) * Φ
Final Answer
- The electric flux for the cube with side '2a' and half the enclosed charge is:
Φ' = Φ / 2
Thus, the correct answer is option 'A' (Φ/2).
Electric flux is defined as the flow of electric field through a surface. According to Gauss's Law, the electric flux (Φ) through a closed surface is proportional to the charge (Q) enclosed by that surface:
Φ = Q / ε₀
where ε₀ is the permittivity of free space.
Scenario 1: Original Cube
- Consider a cube with side length 'a.'
- The electric flux through this cube is given as Φ.
- The charge enclosed in this cube is Q.
Scenario 2: Modified Cube
- The side of the cube is now doubled to '2a.'
- The volume of the cube increases, but the charge enclosed is halved (Q/2).
Applying Gauss's Law
- For the new cube, using Gauss's Law:
Φ' = Q' / ε₀
- Since the new charge Q' = Q/2, we have:
Φ' = (Q/2) / ε₀
Relating New Flux to Original Flux
- The original flux Φ was:
Φ = Q / ε₀
- Therefore, substituting Q' into the equation for the new electric flux:
Φ' = (1/2) * (Q / ε₀) = (1/2) * Φ
Final Answer
- The electric flux for the cube with side '2a' and half the enclosed charge is:
Φ' = Φ / 2
Thus, the correct answer is option 'A' (Φ/2).
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The electric flux from a cube of side ‘a’ is ‘Φ&...
CONCEPT:
Gauss's Law for electric field: It states that the total electric flux emerging out of a closed surface is directly proportional to the charge enclosed by this closed surface. It is expressed as:
ϕ = q/ϵ0
Where ϕ is the electric flux, q is the charge enclosed in the closed surface and ϵ0 is the electric constant.
Given that:
Consider a charge 'q' placed inside a cube of side 'a'.
The electric flux according to Gauss's law,
⇒ ϕ = q/ϵ0
If the charge enclosed is halved, then
⇒ q′ = q/2
Therefore, the new electric flux associated with this,
Gauss's Law for electric field: It states that the total electric flux emerging out of a closed surface is directly proportional to the charge enclosed by this closed surface. It is expressed as:
ϕ = q/ϵ0
Where ϕ is the electric flux, q is the charge enclosed in the closed surface and ϵ0 is the electric constant.
Given that:
Consider a charge 'q' placed inside a cube of side 'a'.
The electric flux according to Gauss's law,
⇒ ϕ = q/ϵ0
If the charge enclosed is halved, then
⇒ q′ = q/2
Therefore, the new electric flux associated with this,
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