Charge A and charge B are 2.00 m apart, and charge A is +3.90 C and charge B is +4.00 C. Charge C is located between them at a certain point and the force on charge C is zero. How far from charge A is charge C?
Find the place where the forces due to A and B are equal and opposite. It will be closer to A than B.
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which method of charge transfer occur when there is no contact between metals a charge by contact b charge by friction c charge by induction
1a 2 c 3 c lesson 1 unit 4
To find the distance of charge C from charge A, we can use Coulomb's law. Coulomb's law states that the force between two charges is given by:
F = k * (|q1| * |q2|) / r^2
Where F is the electrostatic force between the charges, k is the electrostatic constant (9.0 x 10^9 N•m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
In this case, we are given that the force on charge C is zero. This means that the forces exerted by charge A and charge B on charge C cancel each other out:
F_AC + F_BC = 0
To find the distance of charge C from charge A, we need to set up this equation using Coulomb's law:
F_AC = k * (|q_A| * |q_C|) / r_AC^2
F_BC = k * (|q_B| * |q_C|) / r_BC^2
Substituting these equations into the force equation:
k * (|q_A| * |q_C|) / r_AC^2 + k * (|q_B| * |q_C|) / r_BC^2 = 0
Now we can substitute the values given in the problem:
(9.0 x 10^9 N•m^2/C^2) * (3.90 C * |q_C|) / r_AC^2 + (9.0 x 10^9 N•m^2/C^2) * (4.00 C * |q_C|) / r_BC^2 = 0
Since we are looking for the distance of charge C from charge A, let's represent that as r_AC. So we simplify the equation:
(9.0 x 10^9 N•m^2/C^2) * (3.90 C * |q_C|) / r_AC^2 + (9.0 x 10^9 N•m^2/C^2) * (4.00 C * |q_C|) / (2.00 m - r_AC)^2 = 0
Solving this equation will give us the distance of charge C from charge A.