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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 (mass*gravity) and that F=q*E (charge* electric field).
mg=qE
E=mg/q
Plugging in the numbers:
m = 8.2*10^-3 kg
q = -3.3*10^-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?

Respuesta :

Mindaka
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 = (8.2×9.8E-3)/(-3.3E-9) = -2.435E7

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