What is the strength of an electric field that will balance the weight of a 8.2 g plastic sphere that has been charged to - 3.3 nC? Answer in N/C.

Approach: I know that the forces need to balance out, and that F=mg (massgravity) and that F=qE (charge * electric field).

mg=qE

E=mg/q

Plugging in the numbers:

m = 8.210^-3 kg

q = - 3.310^-9 C

g = 9.8*10^-3 N/g

And I get - 24351.5152, but it's wrong. I know there is some error with the units, could someone show me what I am doing wrong?

Question

Deanna Holland

Physics

27 July, 09:05

What is the strength of an electric field that will balance the weight of a 8.2 g plastic sphere that has been charged to - 3.3 nC? Answer in N/C.

Approach: I know that the forces need to balance out, and that F=mg (massgravity) and that F=qE (charge * electric field).

mg=qE

E=mg/q

Plugging in the numbers:

m = 8.210^-3 kg

q = - 3.310^-9 C

g = 9.8*10^-3 N/g

And I get - 24351.5152, but it's wrong. I know there is some error with the units, could someone show me what I am doing wrong?

+2

Answers (1)

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Reginald Mccall · Answer 1

Your approach is correct, but as you thought, the unit of measurement of mass is not in accordance with the unit of measurement of gravity: one is kg, the other one in N/g.

If you bring everything to kg, mass is correct and gravity will be g = 9.8 N/kg.

Therefore:

E = (m·g) / q = (8.2E-3*9.8) / (-3.3E-9) = - 2.435E7

You get the same result if you use grams: m = 8.2g and g = 9.8E-3 N/g:

E = (m·g) / q = (8.2*9.8 E-3) / (-3.3E-9) = - 2.435E7