JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If \(E\) is the electric field and \(\varepsilon_0\) is the permittivity of free space between the plates, then potential energy stored in the capacitor is
- A \(\varepsilon_0 \mathrm{E}^2 \mathrm{Ad}\)
- B \(\frac{1}{2} \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}\)
- C \(\frac{1}{4} \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}\)
- D \(\frac{3}{4} \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2} \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}\)
Step-by-step Solution
Detailed explanation
We know energy density \(\rho_{\mathrm{av}}=\frac{1}{2} \varepsilon_0 E^2\) So potential energy \(=\rho_{a v} \times\) Volume \(\Rightarrow \text { P.E. }=\frac{1}{2} \varepsilon_0 E^2 A d\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is \(\frac{\alpha^{2}}{4} R J / mol\,K\); then the value of \(\alpha\) will be \(.......\) (Assume that the given diatomic gas has no vibrational mode.)JEE Mains 2022 Medium
- Given below are two statements: Statement \(I :\) A second's pendulum has a time period of \(1\) second. Statement \(II :\) It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options given below:JEE Mains 2021 Medium
- Let \(l, r, c\) and \(v\) represent inductance, resistance, capacitance and voltage, respectively. The dimension of \(\frac {l}{rcv}\) in \(SI\,units\) will beJEE Mains 2019 Medium
- The distance between two plates of a capacitor is \(d\) and its capacitance is \(C _1\), when air is the medium between the plates. If a metal sheet of thickness \(\frac{2 d }{3}\) and of same area as plate is introduced between the plates, the capacitance of the capacitor becomes \(C _2\). The ratio \(\frac{ C _2}{ C _1}\) is:JEE Mains 2023 Medium
- A body starts moving from rest with constant acceleration covers displacement \(S_1\) in first \((p-1)\) seconds and \(S_2\) in first \(p\) seconds. The displacement \(S_1+S_2\) will be made in time :JEE Mains 2024 Hard
- In the given electromagnetic wave \(E_y=600 \sin (\omega t-k x) \mathrm{Vm}^{-1}\), intensity of the associated light beam is what? (in \(\mathrm{W} / \mathrm{m}^2\) ); (Given \(\epsilon_0=\) \(\left.9 \times 10^{-12} \mathrm{C}^{-2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)\)JEE Mains 2024 Hard
More PYQs from JEE Mains
- Which one is the correct option for the two different thermodynamic processes ?
JEE Mains 2021 Medium - The rms value of conduction current in a parallel plate capacitor is \(6.9\,\mu\,A\). The capacity of this capacitor, if it is connected to \(230 V\) ac supply with an angular frequency of \(600\,rad / s\), will be \(....\,pF\)JEE Mains 2022 Medium
- The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance asJEE Mains 2023 Medium
- The magnetic field of a plane electromagnetic Wave is \(\overrightarrow{ B }=3 \times 10^{-8} \sin [200 \pi( y + ct )] \hat{ i }\, T\) Where \(c=3 \times 10^{8} \,ms ^{-1}\) is the speed of light. The corresponding electric field isJEE Mains 2020 Hard
- A conductor lies along the \(z-\)axis \(a\) \(-1.5\)\( \le Z < 1.5\,m\) carries a fixed current of \(10.0\ A\) in \( - {\hat a_z}\) direction (see figure). For a field \(\vec B\) \(=\) \(3.0 \times 10^{-4}\) \(e^{-0.2x}\) \({\hat a_y}\,T\) find the power required to move the conductor at constant speed to \(x = 2.0\ m, y = 0\ m\) in \(5 \times 10^{-3}\ s\). Assume parallel motion along the \(x-\)axis........\( W\)
JEE Mains 2014 Hard - The magnetic field in a travelling electromagnetic wave has a peak value of \(20\ n T\). The peak value of electric field strength is......\(Vm^{-1}\)JEE Mains 2013 Easy