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Physics Part-I

Electromagnetic Waves

A parallel plate capacitor with circular plates of radius 1 {~

Physics Part-I

Class 12

NCERT

Chapter 1: Electric Charges and Fields

47 questions

Chapter 2: Electrostatic Potential and Capacitance

46 questions

Chapter 3: Current Electricity

33 questions

Chapter 4: Moving Charges and Magnetism

41 questions

Chapter 5: Magnetism and Matter

36 questions

Chapter 6: Electromagnetic Induction

28 questions

Chapter 7: Alternating Current

37 questions

Chapter 8: Electromagnetic Waves

20 questions

Answer the following questions:

(a) Long distance radio broadcasts use short-wave bands. Why?

(b) It is necessary to use satellites for long distance TV transmission.Why?

(c) Optical and radiotelescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth.Why?

(d) The small ozone layer on top of the stratosphere is crucial for human survival. Why?

(e) If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?

(f) Some scientists have predicted that a global nuclear war on the earth would be followed by a severe nuclear winter with a devastating effect on life on earth. What might be the basis of this prediction?

A parallel plate capacitor with circular plates of radius

1 m

has a capacitance of

1 nF

. At

t = 0

, it is connected for charging in series with a resistor

R = 1 M Ω

across a

2 V

battery (Figure). Calculate the magnetic field at a point

P

, halfway between the centre and the periphery of the plates, after

t = 1 0^{- 3} s

. (The charge on the capacitor at time

t

q (t) = C V [1 - exp (- t / τ)]

, where the time constant

τ

is equal to

CR

A plane electromagnetic wave of frequency

25 MHz

travels in free space along the

x

-direction. At a particular point in space and time,

E = 6.3 j V / m

. What is

B

at this point?

View all question

Question

Medium

Solving time: 3 mins

A parallel plate capacitor with circular plates of radius $1 m$ has a capacitance of $1 nF$ . At $t = 0$ , it is connected for charging in series with a resistor $R = 1 M Ω$ across a $2 V$ battery (Figure). Calculate the magnetic field at a point $P$ , halfway between the centre and the periphery of the plates, after $t = 1 0^{- 3} s$ . (The charge on the capacitor at time $t$ is $q (t) = C V [1 - exp (- t / τ)]$ , where the time constant $τ$ is equal to $CR$ .)

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Updated on: Apr 9, 2023

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Physics Part-I (NCERT)

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A parallel plate capacitor with circular plates of radius

1 m

has a capacitance of

1 nF

. At

t = 0

, it is connected for charging in series with a resistor

R = 1 M Ω

across a

2 V

battery (Figure). Calculate the magnetic field at a point

P

, halfway between the centre and the periphery of the plates, after

t = 1 0^{- 3} s

. (The charge on the capacitor at time

t

q (t) = C V [1 - exp (- t / τ)]

, where the time constant

τ

is equal to

CR

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

The time constant of the

CR

circuit is

τ = CR = 1 0^{- 3} s

. Then, we have

q (t) = C V [1 - exp (- t / τ)]

= 2 \times 1 0^{- 9} [1 - exp (- t /1 0^{- 3})]

The electric field in between the plates at time

t

E = \frac{q ( t )}{ε _{0} A} = \frac{q}{π ε _{0}}; A = π (1)^{2} m^{2} =

area of the plates. Consider now a circular loop of radius

(1/2) m

parallel to the plates passing through

P

. The magnetic field

B

at all points on the loop is along the loop and of the same value. The flux

Φ_{E}

through this loop is

Φ_{E} = E \times

area of the loop

= E \times π \times (\frac{1}{2})^{2} = \frac{π E}{4} = \frac{q}{4 ε _{0}}

The displacement current

i_{d} = ε_{0} \frac{d Φ _{E}}{d t} = \frac{1}{4} \frac{d q}{d t} = 0.5 \times 1 0^{- 6} exp (- 1)

t = 1 0^{- 3} s

. Now, applying Ampere-Maxwell law to the loop, we get

B \times 2 π \times (\frac{1}{2}) = μ_{0} (i_{c} + i_{d}) = μ_{0} (0 + i_{d}) = 0.5 \times 1 0^{- 6} μ_{0} exp (- 1)

or, B = 0.74 \times 1 0^{- 13} T

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Practice more questions from Physics Part-I (NCERT)

Answer the following questions:

(a) Long distance radio broadcasts use short-wave bands. Why?

(b) It is necessary to use satellites for long distance TV transmission.Why?

(c) Optical and radiotelescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth.Why?

(d) The small ozone layer on top of the stratosphere is crucial for human survival. Why?

(e) If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?

A parallel plate capacitor with circular plates of radius

1 m

has a capacitance of

1 nF

. At

t = 0

, it is connected for charging in series with a resistor

R = 1 M Ω

across a

2 V

battery (Figure). Calculate the magnetic field at a point

P

, halfway between the centre and the periphery of the plates, after

t = 1 0^{- 3} s

. (The charge on the capacitor at time

t

q (t) = C V [1 - exp (- t / τ)]

, where the time constant

τ

is equal to

CR

A plane electromagnetic wave of frequency

25 MHz

travels in free space along the

x

-direction. At a particular point in space and time,

E = 6.3 j V / m

. What is

B

at this point?

View all

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Question Text	A parallel plate capacitor with circular plates of radius $1 m$ has a capacitance of $1 nF$ . At $t = 0$ , it is connected for charging in series with a resistor $R = 1 M Ω$ across a $2 V$ battery (Figure). Calculate the magnetic field at a point $P$ , halfway between the centre and the periphery of the plates, after $t = 1 0^{- 3} s$ . (The charge on the capacitor at time $t$ is $q (t) = C V [1 - exp (- t / τ)]$ , where the time constant $τ$ is equal to $CR$ .)
Updated On	Apr 9, 2023
Topic	Electromagnetic Waves
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 11
Upvotes	1294
Avg. Video Duration	14 min

Text solutionVerified

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