AP Physics C E and M

Question

Multiple Choice

Three-point charges are located along the x-axis: q₁ = +5.0 μC is at 20 cm, q₂ = +4.0 μC is at 0 cm, and q₃ = +10.0 μC is at –30 cm. What is the electrostatic force exerted on q₂ by q₃?

a) 4.0 N to the right

 

b)  4000 N to the right

 

c)  4000 N to the left

 

 d) 4.0 N to the left

 

Answer 1

In this problem, there are three point charges which are all located along the same line. For each of the three charges we are given information about their position and their charge.

Our deliverable for this problem is to determine the magnitude and direction of the electrostatic force that Charge #3 (q₃) exerts onto Charge #2 (q₂).

Since in this problem we don't care about anything pertaining to Charge #1, we can go ahead and ignore all information about Charge #1's position and charge.

Now, let's take a look at Charge #2 and #3's given information:

1. q₂ = +4.0 µC ; X₂ = 0 cm (charge #2 is at the "origin")
2. q₃ = +10.0 µC ; X₃ = -30 cm (charge #3 is to the left of the origin)

Before we use any electrostatic force formulas, let's use our intuition to see which direction we expect that Charge #3 should push Charge #2. Both charges are of the same sign (they are both positive), and thus they should repel each other. Since Charge #3 is to the left of Charge #2, we should expect that Charge #3 should repel Charge #2 to the right.

Now, let's hold onto that intuition and jump into the math!

The formula for electrostatic force is called Coulomb's Law and is written as:

F = (kq₁q₂)/ r²

Where F is the magnitude of the electrostatic force, k is a constant called Coulomb's constant which is equal to 8.99 x 10⁹ Nm²/C, q₁ is the charge of the 1st particle, q₂ is the charge of the 2nd particle, and r is the distance between the particles. Note that the "order" of which particle we chose to be "first" is not important for the usage of this formula.

In this problem, we can calculate the "r" value as r = X₂ - X₃ = (0 cm) - ( -30 cm) = +30 cm

One final step we need to consider before we plug our numbers into Coulomb's Law: Not all the numbers in this problem are in a nicest, most basic metric form! We will get an answer with weird, awkward units if we plug in all our numbers without converting them to their most basic metric units.

r = 30 cm = 0.30 m

q₂ = +4.0 µC = +4.0 x 10^-6 C

q₃ = +10.0 µC = +10.0 x 10^-6 C

Let's now plug in our values to Coulomb's Law!

F = (kq₁q₂)/ r² = [(8.99 x 10⁹ Nm²/C)*(4.0 x 10^-6 C)*(10.0 x 10^-6 C)] / (0.30 m)²

F = 3.995 N ≈ 4 N

So we calculate that the magnitude of the electrostatic force exerted by Charge #3 onto Charge #2 is 4 N. Our earlier discussion tells us that this force must be pushing Charge #2 to the right. Putting the magnitude and direction answers together we get that the answer should be (a) 4.0 N to the right.

Extra info: Newton's 3rd Law says that "For every action there must be an equal and opposite reaction". We can see Newton's 3rd Law in action if we ask ourselves "What is the magnitude and direction of the force that Charge #2 exerts BACK onto Charge #3?". Now we could work EVERYTHING our again, or we can use our knowledge of Newton's 3rd Law to know that Charge #2 exerts an EQUAL force (4 N) in an opposite direction (to the left) onto Charge #3. Saves a lot of time right?

Hope that helps!

--Zach