The figure below shows a test charge q between the two positive charges. Find the force (in newtons) on the test charge for q = 1 µC. Give a positive answer if the force is to the right and a negative answer if the force is to the left.

2µC....-3cm-....q...-2cm-...3µC

the force on q from the charge on the left is to the right, the force on q from the charge on the right is to the left.

Force=forceleftcharge - forcerightcharge
= k 2E-6*E-6/.03^2 -k2E-6*E-6/.02^2

thank you=]

it seems i got it incorrect i had put 47.44722

nvm i did bad arithmetic... stupid mistake thank you

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What was the answer?

k 2E-6*E-6/.03^2 -k3E-6*E-6/.02^2

if your q is positive then your answer is negative

why isnt the answer 47

To find the force on the test charge, we can use Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Let's break down the given information:
- Test charge (q) = 1 µC (microcoulombs)
- Positive charge (+2µC) located 3 cm to the left of the test charge
- Positive charge (+3µC) located 2 cm to the right of the test charge

Step 1: Calculate the distances between the test charge and each positive charge.
- Distance between the test charge and the +2µC charge = 3 cm = 0.03 m (converting cm to meters)
- Distance between the test charge and the +3µC charge = 2 cm = 0.02 m (converting cm to meters)

Step 2: Calculate the magnitudes of the forces between the test charge and each positive charge using Coulomb's law.
- Force due to the +2µC charge = k * (q1 * q2) / r^2, where k is the electrostatic constant (approximated as 9 × 10^9 N m^2/C^2)
Plugging in the values: Force = (9 * 10^9 N m^2/C^2) * ((1 µC) * (2 µC)) / (0.03 m)^2

- Force due to the +3µC charge = k * (q1 * q2) / r^2, using the given values: Force = (9 * 10^9 N m^2/C^2) * ((1 µC) * (3 µC)) / (0.02 m)^2

Step 3: Calculate the net force on the test charge by adding or subtracting the magnitudes of the forces. Use the convention that forces to the right are positive and forces to the left are negative.
- Net Force = Force due to the +3µC charge - Force due to the +2µC charge

Once you plug in the values and perform the calculations, you will have the answer to the question.