Mastering Physics Solutions: Problem 26.67

Problem 26.67

Part A = 180 nC m Click to use the calculator/solver for this part of the problem

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.

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

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