If the net electric field at point P along Y axis is zero, then the ratio of |q₂/q₃| is 8/(5 √x), where x= ________.

Solution

Physics sir · 4 steps

Split each field into components; only the vertical parts must cancel at P.

1. Distances to P. Take the foot of the perpendicular as the origin, so q₂ is at (-2, 0), q₃ at (3, 0) and P at (0, 4), all in cm. Then r₂ = √(2² + 4²) = 2√5 and r₃ = √(3² + 4²) = 5.
2. Field directions. The field of +q₂ points away from it, up and to the right, with sin θ₂ = 4/2√5 = 2/√5. The field of -q₃ points towards it, down and to the right, with sin θ₃ = 4/5. Both horizontal parts point right and add, so only the vertical parts can cancel.

   (k q₂)/(2√5)²·2/√5 = (k q₃)/5²·4/5

3. Simplify. The left side is (k q₂)/10√5 and the right side is (4 k q₃)/125. So |q₂/q₃| = 40√5/125 = 8√5/25 = 8/5√5.
4. So. Comparing with 8/5√x gives x = 5.

The idea to keep. When a field is zero along one direction, resolve each charge's field and balance only those components. Each field is kq/r² times the sine or cosine of its angle, never the bare kq/r².

Answer from the NTA final answer key. Solution by PrepWiser.