Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and is the permittivity of free space between the plates, then potential energy stored in the capacitor is [2025]

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Q.
Consider a parallel plate capacitor of area A (of each plate) and separation $' d'$ between the plates. If E is the electric field and $ε_{0}$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is [2025]

1 $\frac{1}{2} ε_{0} E^{2} A d$

2 $\frac{3}{4} ε_{0} E^{2} A d$

3 $\frac{1}{4} ε_{0} E^{2} A d$

4 $ε_{0} E^{2} A d$

Ans.
(1)

We know energy density

$ρ_{av} = \frac{1}{2} ε_{0} E^{2}$

So potential energy $= ρ_{av} \times$ Volume

$\Rightarrow P . E . = \frac{1}{2} ε_{0} E^{2} A d$

Solution

Q.
Consider a parallel plate capacitor of area A (of each plate) and separation $' d'$ between the plates. If E is the electric field and $ε_{0}$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is [2025]

1 $\frac{1}{2} ε_{0} E^{2} A d$

2 $\frac{3}{4} ε_{0} E^{2} A d$

3 $\frac{1}{4} ε_{0} E^{2} A d$

4 $ε_{0} E^{2} A d$

Ans.
(1)

We know energy density

$ρ_{av} = \frac{1}{2} ε_{0} E^{2}$

So potential energy $= ρ_{av} \times$ Volume

$\Rightarrow P . E . = \frac{1}{2} ε_{0} E^{2} A d$

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Solution

Q. Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and ε0 is the permittivity of free space between the plates, then potential energy stored in the capacitor is [2025]

1 12ε0E2Ad

2 34ε0E2Ad

3 14ε0E2Ad

4 ε0E2Ad

Ans. (1) We know energy density ρav=12ε0E2 So potential energy =ρav× Volume ⇒ P.E.=12ε0E2Ad

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Q.
Consider a parallel plate capacitor of area A (of each plate) and separation $' d'$ between the plates. If E is the electric field and $ε_{0}$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is [2025]

1 $\frac{1}{2} ε_{0} E^{2} A d$

2 $\frac{3}{4} ε_{0} E^{2} A d$

3 $\frac{1}{4} ε_{0} E^{2} A d$

4 $ε_{0} E^{2} A d$

Ans.
(1)

We know energy density

$ρ_{av} = \frac{1}{2} ε_{0} E^{2}$

So potential energy $= ρ_{av} \times$ Volume

$\Rightarrow P . E . = \frac{1}{2} ε_{0} E^{2} A d$