The magnetic field of a plane electromagnetic wave is given by:
\[
\vec{B} = 2 \times 10^{-8} \sin \left(0.5 \times 10^3 x + 1.5 \times 10^{11} t \right) \hat{j} \, {T}.
\]
{The amplitude of the electric field would be:}
Show Hint
- \( 6 \, {V/m} \, {along x-axis} \)
- \( 3 \, {V/m} \, {along z-axis} \)
- \( 6 \, {V/m} \, {along z-axis} \)
- \( 2 \times 10^{-8} \, {V/m} \, {along z-axis} \)
The Correct Option is A
Solution and Explanation
Step 1: The relationship between the electric field \( E \) and the magnetic field \( B \) in a plane electromagnetic wave is given by: \[ E = c B \] where \( c = 3 \times 10^8 \, {m/s} \) is the speed of light.
Step 2: Given that the amplitude of the magnetic field is \( 2 \times 10^{-8} \, {T} \), we can calculate the amplitude of the electric field as: \[ E = (3 \times 10^8) \times (2 \times 10^{-8}) = 6 \, {V/m}. \]
Step 3: Since the magnetic field is along the \( \hat{j} \)-axis (the \( y \)-axis), the electric field must be perpendicular to it and, therefore, must be along the \( x \)-axis.
Top VITEEE Physics Questions
- A motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times, the power of the motor is increased to $P_1$. The ratio of $P_1 $ to $P_0$ is
- A $30\,V-90\,W$ lamp is operated on a $120\,V$ DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance is
- The masses of three copper wires are in the ratio $2 : 3 : 5$ and their lengths are in the ratio $5 : 3 : 2$ .Then, the ratio of their electrical resistances is
- A soap bubble of radius $r$ is blown up to form a bubble of radius $2 r$ under isothermal conditions. If $T$ is the surface tension of soap solution, the energy spent in the blowing
- A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given, surface tension of liquid T, density $\rho$)
Top VITEEE LCR Circuit Questions
- The current in an $L-R$ circuit builds up to $\left(3 / 4^{\text {th }}\right)$ of its steady state value in $4$ seconds. The time constant of this circuit is
- The self-induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10A to 25 A in 1s, the change in the energy of the inductance is:
- Which of the following figure represents the variation of \( \ln \left( \frac{R}{R_0} \right) \) with \( \ln A \) (If \( R \) is the radius of a nucleus and \( A \) is its mass number)?
- A particle is moving with a velocity \( \vec{v} = K (y \hat{i} + x \hat{j} )\), where \( K \) is a constant. The general equation for its path is:
A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be:
Top VITEEE Questions
- A motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times, the power of the motor is increased to $P_1$. The ratio of $P_1 $ to $P_0$ is
- A $30\,V-90\,W$ lamp is operated on a $120\,V$ DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance is
- Which of the following is not a characteristic of transition elements ?
- Most crystals show good cleavage because their atoms, ions or molecules are
- Which of the following sets consists only of essential amino acids ?