Question:medium

Point charge of \( 10 \, \mu C \) is placed at the origin. At what location on the X-axis should a point charge of \( 40 \, \mu C \) be placed so that the net electric field is zero at \( x = 2 \, \text{cm} \) on the X-axis?

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When determining the position for zero net electric field, equate the magnitudes of electric fields from the charges and carefully solve the resulting equation. Consider the geometry and direction of forces to select the correct solution.
Updated On: Nov 26, 2025
  • \( 6 \, \text{cm} \)
  • \( 4 \, \text{cm} \)
  • \( 8 \, \text{cm} \)
  • \( -4 \, \text{cm} \)
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The Correct Option is A

Solution and Explanation

To determine the position \(x_0\) for the second charge (\(40 \, \mu \text{C}\)) where the net electric field is zero at \(x = 2 \, \text{cm}\): Step 1: Equate Electric Field Magnitudes The net electric field is zero when the magnitudes of the fields from both charges are equal: \[K \cdot \frac{10 \times 10^{-6}}{(2)^2} = K \cdot \frac{40 \times 10^{-6}}{(x_0 - 2)^2}.\] Step 2: Simplify the Expression Cancel \(K\) and simplify the numerical values: \[\frac{10}{4} = \frac{40}{(x_0 - 2)^2}.\] Further simplification yields: \[\frac{1}{2} = \frac{2}{(x_0 - 2)^2}.\] Step 3: Solve for \(x_0\) Rearrange the equation to isolate \( (x_0 - 2)^2 \): \[(x_0 - 2)^2 = 4.\] Taking the square root of both sides gives: \[x_0 - 2 = \pm 2.\] The possible values for \(x_0\) are: \[x_0 = 4 \, \text{cm} \quad \text{or} \quad x_0 = 6 \, \text{cm}.\] Step 4: Select the Valid Position Given that the second charge is located to the right of \(x = 2 \, \text{cm}\), the correct position is: \[x_0 = 6 \, \text{cm}.\] Final Answer: \[\boxed{x_0 = 6 \, \text{cm}}\]
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