Question:
If two electromagnetic waves with electric fields given by
$$
\vec{E_1} = E_0 \sin (kx - \omega t) \hat{j}
$$
and
$$
\vec{E_2} = E_0 \sin (kx - \omega t + \pi) \hat{j}
$$
- interfere, then the peak value of the electric field of the resultant wave is
If two electromagnetic waves with electric fields given by
$$
\vec{E_1} = E_0 \sin (kx - \omega t) \hat{j}
$$
and
$$
\vec{E_2} = E_0 \sin (kx - \omega t + \pi) \hat{j}
$$
- interfere, then the peak value of the electric field of the resultant wave is
Show Hint
When two waves with equal amplitude and opposite phase (\(\pi\) phase difference) interfere, they cancel each other completely, leading to a resultant electric field of zero.
Updated On: May 5, 2026
- \(E_0\)
- \(\frac{E_0}{2}\)
- \(\frac{E_0}{\sqrt{2}}\)
- Zero
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Identify phase difference
The two waves are: \[ E_1 = E_0 \sin(kx - \omega t), \quad E_2 = E_0 \sin(kx - \omega t + \pi) \] Phase difference: \[ \Delta \phi = \pi \]
Step 2: Use interference result formula
Resultant amplitude for two waves: \[ R = 2E_0 \cos\left(\frac{\Delta \phi}{2}\right) \]
Step 3: Substitute value
\[ R = 2E_0 \cos\left(\frac{\pi}{2}\right) = 2E_0 \times 0 = 0 \]
Step 4: Result
Since amplitude is zero, resultant electric field is zero.
Final Answer: Zero
The two waves are: \[ E_1 = E_0 \sin(kx - \omega t), \quad E_2 = E_0 \sin(kx - \omega t + \pi) \] Phase difference: \[ \Delta \phi = \pi \]
Step 2: Use interference result formula
Resultant amplitude for two waves: \[ R = 2E_0 \cos\left(\frac{\Delta \phi}{2}\right) \]
Step 3: Substitute value
\[ R = 2E_0 \cos\left(\frac{\pi}{2}\right) = 2E_0 \times 0 = 0 \]
Step 4: Result
Since amplitude is zero, resultant electric field is zero.
Final Answer: Zero
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