**Problem 26.67**

**Solution Below:**

An electric field E = 100,000i N/C causes the 5.0 g point charge in the figure to hang at a 20° angle.

Part A

What is the charge on the ball?

Express your answer using two significant figures.

Express your answer using two significant figures.

We can solve this by using tension. You know that the force of gravity equals tension * cos(θ):

Tcos(θ) = mg

T * cos(20) = 0.005 * 9.81

T = (0.005 * 9.81) / cos(20)

T = 0.05220

And we also know that since the electric field/force is in the X direction:

T * sin(20) = E

Where E is the electric force

So plug in for T and solve for the electric force:

T * sin(20) = E

0.05220 * sin(20) = E

E = 0.01785 N

Since the field is in N/C (newtons per coulomb) and the force is in Newtons:

100,000 N/C = 0.01785 / X

X * 100,000 = 0.01785

X = 0.01785 / 100,000

X = 0.0000001785

Make sure to round to 2 significant figures like the problem asks for!

X = 180 nC

180 nC