Answer:
1782.7 N/C, downward
Explanation:
Since the charged sphere is in static equilibrium, it means that the electric force acting is balanced with the weight of the sphere, so we can write:
[tex]F_G = F_E\\mg = qE[/tex]
where
m = 3.62 g = 0.00362 kg is the mass of the sphere
g = 9.8 m/s^2 is the acceleration of gravity
[tex]q=19.9 \mu C= 19.9\cdot 10^{-6}C[/tex] is the magnitude of the charge
E is the magnitude of the electric field
Solving for E,
[tex]E=\frac{mg}{q}=\frac{(0.00362 kg)(9.8 m/s^2)}{19.9\cdot 10^{-6} C}=1782.7 N/C[/tex]
In order for the sphere to be in equilibrium, the electric force must be in opposite direction to the weight, so the electric force must point upward. Since the sphere has a negative charge, the electric field has opposite direction to the electric force: so, the electric field direction is downward.
The magnitude of the electric field is 1782.7 N/C. The direction of the electric field is in the downward direction due to the negative charge on the charged sphere.
The magnitude of an electric field refers to the force in each electric charge on the test charge.
From the parameters given:
Thus, the magnitude of the electric field can be computed by using the formula:
[tex]\mathbf{E =\dfrac{F}{q}}[/tex]
[tex]\mathbf{E =\dfrac{m \times g}{q}}[/tex]
[tex]\mathbf{E =\dfrac{0.00362 \ kg \times 9.8 \ m/s^2}{19.9\times 10^{-6} C}}[/tex]
E = 1782.71 N/C
However, the direction of the electric field is in the downward direction due to the negative charge on the charged sphere.
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