A positive charge of 1.100ƒÊ C is located in a uniform field of 1.10�~105 N/C. A negative charge of -0.100ƒÊ C is brought near enough to the positive charge that the attractive force between the charges just equals the force on the positive charge due to the field. How close are the two charges?
So the negative force must be creating a field of 1.10E5 N/C in the opposite direction.
1.10E5=k (.1C)/distance^2
so would the answer be positive?
Huh? The question asks for a distance.
To find the distance between the two charges, let's break down the problem into a few steps:
Step 1: Calculate the electric force between the positive charge and the negative charge.
The formula to calculate the electric force is given by:
F = k * (|q1| * |q2|) / r^2
Where:
F is the electric force between the charges,
k is the Coulomb's constant, approximately 9 * 10^9 Nm^2/C^2,
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
In this step, we'll use the fact that the attractive force between the charges just equals the force on the positive charge due to the field. So:
F (electric force) = F (force due to the electric field)
Step 2: Find the force on the positive charge due to the electric field.
The force on a charge due to an electric field is given by:
F = q * E
Where:
F is the force on the charge,
q is the magnitude of the charge, and
E is the electric field strength.
Step 3: Equate the forces from Step 1 and Step 2 and solve for the distance between the charges (r).
Now, let's plug in the given values and solve the problem:
Step 1: Calculate the electric force between the charges.
F = k * (|q1| * |q2|) / r^2
F = k * (1.100 * 10^-6 C * 0.100 * 10^-6 C) / r^2
Step 2: Find the force on the positive charge due to the electric field.
F = q * E
F = 1.100 * 10^-6 C * 1.10 * 10^5 N/C
Step 3: Equate the forces and solve for the distance (r).
k * (1.100 * 10^-6 C * 0.100 * 10^-6 C) / r^2 = 1.100 * 10^-6 C * 1.10 * 10^5 N/C
Now, we can solve this equation for r.