Home
Class 12
PHYSICS
A plane EM wave travelling in vacuum alo...

A plane EM wave travelling in vacuum along z - direction is given by `vec(E )=E_(0)sin (kz - omega t)hat(i)` and `vec(B)=B_(0)sin(kz - omega t)hat(j)`.

Use equation `int vec(E ).vec(d)l =-(d phi_(B))/(dt)` to prove `(E_(0))/(B_(0))=c`.

Text Solution

Verified by Experts

Now `oint vec(E ).vec(d)l = -(d)/(dt)oint vec(B).vec(d )s`
`thereofre` From equation (1) and (2),
`E_(0)h[sin (kz_(2)-omega t)-sin (kz_(1)-omega t)] =-(d)/(dt)`
`[(B_(0)h)/(k){cos (kz_(2)-omega t)-cos(kz_(1)-wt)}]`
`therefore E_(0)h[sin(kz_(2)-omega t)-sin (kz_(1)-omega t)]`
`=(B_(0)h)/(k)(omega)[sin (kz_(2)-omega t)-sin (kz_(1)-omega t)]`
`therefore E_(0)h=R_(0)h((omega)/(k))`
`therefore E_(0)=B_(0)c " " [because (omega)/(k)=c]`
`therefore (E_(0))/(B_(0))=c`
Promotional Banner

Topper's Solved these Questions

  • ELECTROMAGNETIC WAVES

    KUMAR PRAKASHAN|Exercise SECTION D MULTIPLE CHOICE QUESTIONS (MCQs)|76 Videos

  • ELECTROMAGNETIC WAVES

    KUMAR PRAKASHAN|Exercise SECTION D MULTIPLE CHOICE QUESTIONS (MCQs) MCQs asked in Competitive Exams|23 Videos

  • ELECTROMAGNETIC WAVES

    KUMAR PRAKASHAN|Exercise SECTION C NCERT EXEMPLAR SOLUTION (Short Answer Type Questions)|9 Videos

  • ELECTROMAGNETIC INDUCTION

    KUMAR PRAKASHAN|Exercise Section D MCQs (MCQs asked in Competitive Exams )|38 Videos

  • ELECTROSTATIC POTENTIAL AND CAPACITANCE

    KUMAR PRAKASHAN|Exercise Section D ( MCQs asked in Cometitive Exams )|39 Videos

Similar Questions

Explore conceptually related problems

A plane EM wave travelling in vacuum along z - direction is given by vec(E )=E_(0)sin (kz - omega t)hat(i) and vec(B)=B_(0)sin(kz - omega t)hat(j) . By using similar process and the equation int vec(B).vec(d)l = mu_(0)I+ in_(0)(d phi_(E ))/(dt) , prove that c=(1)/(sqrt(mu_(0)in_(0)))

A plane EM wave travelling in vacuum along z - direction is given by vec(E )=E_(0)sin (kz - omega t)hat(i) and vec(B)=B_(0)sin(kz - omega t)hat(j) . Evaluate int vec(E ). Vec(d)l over the rectangular loop 134 shown in figure.

A plane EM wave travelling in vacuum along z - direction is given by vec(E )=E_(0)sin (kz - omega t)hat(i) and vec(B)=B_(0)sin(kz - omega t)hat(j) . Evaluate int vec(B).vec(d)s over the surface bounded by loop 1234.

A plane EM wave travelling along z - direction is desctribed vec(E )=E_(0)sin(kz - omega t)hat(i) and veC(B)=B_(0)sin (kz - omega)hat(j) . Show that The time averaged intensity of the wave is given by I_(av)=(1)/(2)c in_(0)E_(0)^(2) .

A plane EM wave travelling along z - direction is desctribed vec(E )=E_(0)sin(kz - omega t)hat(i) and veC(B)=B_(0)sin (kz - omega)hat(j) . Show that The average energy density of the wave is given by U_(av)=(1)/(4)in_(0)E_(0)^(2)+(1)/(4).(B_(0)^(2))/(mu_(0)) .

An electromagnetic wave travels in vacuum along z - direction : vec(E )=(E_(1)hat(i)+E_(2)hat(j))cos(kz-omega t) . Choose the correct options from the following :

A plane electromagnetic wave propagating along x - direction can have the following pairs of vec(E ) and vec(B) .

A particle is moving with a position vector, vec(r)=[a_(0) sin (2pi t) hat(i)+a_(0) cos (2pi t) hat(j)] . find Distance travelled by the particle in 1 sec is

A transverse wave travelling along the positive x-axis, given by y=A sin (kx - omega t) is superposed with another wave travelling along the negative x-axis given by y=A sin (kx + omega t) . The point x=0 is

Given magnetic field equation is vec(B)=3xx10^(-8) sin[omega t-kx + phi] hat(j) then appropriate equation for electric field (vec(E )) will be …….