Question

The square of resultant of two equal electric field vectors is three times their product. Angle between them is

• A. \( \frac{\pi}{5} \)
• B. \( \frac{\pi}{6} \)
• C. \( \frac{\pi}{8} \)
• D. \( \frac{\pi}{3} \)

Hint:

Use vector addition formula \( R^2 = A^2 + B^2 + 2AB\cos\theta \) when magnitudes are equal.

Answer 1

The Correct Option is D

Step 1: Write formula for resultant of two vectors.
For two vectors \( E \) and \( E \):
\[ R^2 = E^2 + E^2 + 2E^2 \cos\theta \]

Step 2: Simplify expression.
\[ R^2 = 2E^2(1 + \cos\theta) \]

Step 3: Use given condition.
\[ R^2 = 3E^2 \]

Step 4: Equate both expressions.
\[ 2E^2(1 + \cos\theta) = 3E^2 \]

Step 5: Cancel common terms.
\[ 2(1 + \cos\theta) = 3 \]

Step 6: Solve for \( \cos\theta \).
\[ 1 + \cos\theta = \frac{3}{2} \] \[ \cos\theta = \frac{1}{2} \]

Step 7: Find angle.
\[ \theta = \frac{\pi}{3} \]