Question

Two point charges -10 µC and +5 µC are situated on the X-axis at \( x = 0 \) and \( x = \sqrt{2} \, \text{m} \). The point along the X-axis where the electric field becomes zero is.

• A. \( x = \left( \sqrt{2} - 1 \right) \, \text{m} \)
• B. \( x = 2 \left( \sqrt{2} - 1 \right) \, \text{m} \)
• C. \( x = 2 \left( \sqrt{2} + 1 \right) \, \text{m} \)
• D. \( x = \left( \sqrt{2} + 1 \right) \, \text{m} \) \bigskip

Hint:

Set the electric fields due to two charges equal and solve for the point where they cancel each other out to find the location of zero field.

Answer 1

The Correct Option is C

Step 1: To find the point where the electric field is zero, we must equate the electric fields due to both charges. The electric field due to a point charge is given by: \[ E = \frac{k \cdot q}{r^2} \] where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge. The point where the electric field becomes zero is where the magnitudes of the fields from both charges are equal, so: \[ \frac{k \cdot 10 \times 10^{-6}}{x^2} = \frac{k \cdot 5 \times 10^{-6}}{(x - \sqrt{2})^2} \] After solving the equation, we get the value \( x = 2(\sqrt{2} + 1) \, \text{m} \).