A light beam traveling in the x-direction is described by the magnetic field \( B_z = 2 \times 10^{-6} \sin \omega(t - x/c) \) Tesla. The value of the maximum electric field is
Show Hint
- 200 V/m
- 300 V/m
- 600 V/m
- 800 V/m
The Correct Option is C
Solution and Explanation
Step 1: State the relationship between the amplitudes of electric and magnetic fields in an electromagnetic wave. In a vacuum (or air, approximately), the magnitudes of the electric field (\(E\)) and magnetic field (\(B\)) at any instant are related by: \[ E = cB \] where \(c\) is the speed of light. This relationship also holds for their maximum values (amplitudes), \(E_0\) and \(B_0\). \[ E_0 = c B_0 \]
Step 2: Identify the maximum magnetic field (\(B_0\)) from the given equation. The equation for the magnetic field is given in the form \( B_z = B_0 \sin(\dots) \). By comparing, we can see that the amplitude (maximum value) of the magnetic field is \( B_0 = 2 \times 10^{-6} \) T.
Step 3: Calculate the maximum electric field (\(E_0\)). Use the value of the speed of light, \( c \approx 3 \times 10^8 \) m/s. \[ E_0 = (3 \times 10^8 \text{ m/s}) \times (2 \times 10^{-6} \text{ T}) \] \[ E_0 = 6 \times 10^2 \text{ V/m} = 600 \text{ V/m} \]
Top Questions on Electromagnetism
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \), where \( \omega \) is the frequency of the supply across resistor \( R \) and inductor \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In light of the above statements, choose the most appropriate answer from the options given below:
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