A parallel plate capacitor has plate area A and plate separation d. It is connected to a battery of emf V and internal resistance R, at time t=0. Consider a plane surface of area 2A, parallel to the plates and located symmetrically between them. Find the displacement current through the surface as a function of time.

Charge on the capacitor plate varies with time as Charging current is i=dtdq=RVe−t/RC The electric field between the plates is E=Aε0q Flux through area A/2 is ϕE=E2A=2ε0q The displacement currrent through the area A/2 is id=ε0dtdϕE=ε02ε01dtdq=21i or, id=2RVe−t/RC=2RVe−ε0ARtd[∵C=dε0A]

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Class 12

Physics

Electromagnetic Waves

Displacement current

A parallel plate capacitor has plate area A and plate separati

Question

Medium

Solving time: 3 mins

A parallel plate capacitor has plate area $A$ and plate separation $d$ . It is connected to a battery of emf $V$ and internal resistance $R$ , at time $t = 0$ . Consider a plane surface of area $\frac{A}{2}$ , parallel to the plates and located symmetrically between them. Find the displacement current through the surface as a function of time.

Views: 5,998 students

Book:

Physics for JEE Main and Advanced Magnetism and EMI (McGraw Hill)

Found 4 tutors discussing this question

Isabella Discussed

A parallel plate capacitor has plate area

A

and plate separation

d

. It is connected to a battery of emf

V

and internal resistance

R

, at time

t = 0

. Consider a plane surface of area

\frac{A}{2}

, parallel to the plates and located symmetrically between them. Find the displacement current through the surface as a function of time.

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Charge on the capacitor plate varies with time as Solution Image

Charging current is

i = \frac{d q}{d t} = \frac{V}{R} e^{- t / RC}

The electric field between the plates is

E = \frac{q}{A ε _{0}}

Flux through area

A /2

ϕ_{E} = E \frac{A}{2} = \frac{q}{2 ε _{0}}

The displacement currrent through the area

A /2

i_{d} = ε_{0} \frac{d ϕ _{E}}{d t} = ε_{0} \frac{1}{2 ε _{0}} \frac{d q}{d t} = \frac{1}{2} i

or, i_{d} = \frac{V}{2 R} e^{- t / RC} = \frac{V}{2 R} e^{- \frac{t d}{ε _{0} A R}} [∵ C = \frac{ε _{0} A}{d}]

Was this solution helpful?

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our Physics tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	A parallel plate capacitor has plate area $A$ and plate separation $d$ . It is connected to a battery of emf $V$ and internal resistance $R$ , at time $t = 0$ . Consider a plane surface of area $\frac{A}{2}$ , parallel to the plates and located symmetrically between them. Find the displacement current through the surface as a function of time.
Topic	Electromagnetic Waves
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	77

Text solutionVerified

Practice questions from Physics for JEE Main and Advanced Magnetism and EMI (McGraw Hill)

Practice more questions from Electromagnetic Waves

Practice questions on similar concepts asked by Filo students

Text solutionVerified

Practice questions from Physics for JEE Main and Advanced Magnetism and EMI (McGraw Hill)

Practice more questions from Electromagnetic Waves

Practice questions on similar concepts asked by Filo students

Related books for questions on Electromagnetic Waves