Question

An electric field E? =100,000?^N/C causes the 5.0 gpoint charge in the figure (Figure 1) to hang at a 20?angle.

What is the charge on the ball?

Express your answer to two significant figures and include the appropriate units.

Answer 1

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

Tcos(?) = 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

Answer 2

T*cos(20 deg) = mg

T = 5*10^-3 * 9.8 / cos(20 deg) = 0.052144 N

T*sin(20 deg) = E*q

q = 0.052144*sin(20 deg) / 100000 = 1.783 * 10^-7 C

q = 0.18 uC

Answer 3

2 x 10^-2 uC

Answer 4

0.18 uC

Answer 5

0.1813 uC

Answer 6

18 C