Two charges of 2.0 10⁻⁶ C and 1.0 10⁻⁶ C are located at a separation of 10 cm . Determine where a third charge must be placed so that it experiences zero net force from these two charges.

Step-by-step solution

Let the third charge q be placed at a distance x from the larger charge q₁ = 2.0 10⁻⁶ C . The distance from the smaller charge q₂ = 1.0 10⁻⁶ C will be (10 - x) cm . For the net force on q to be zero, the electrostatic forces due to q₁ and q₂ must be equal in magnitude and opposite in direction: k q₁ q x^2 = k q₂ q (10 - x)^2 Substituting the given values: 2.0 10⁻⁶ x^2 = 1.0 10⁻⁶ (10 - x)^2 2 x^2 = 1 (10 - x)^2 Taking the square root of both sides: 2 x = 1 10 - x 10 2 - 2 x = x x( 2 + 1) = 10 2 x = 10 2 2 + 1 Ration