Final answer:
The strength of the electric field needed to balance the weight of a 9.2 g plastic sphere charged to -5.2 nC is approximately 17.36 x 10^6 N/C.
Step-by-step explanation:
To find the strength of an electric field that will balance the weight of a charged plastic sphere, we need to equate the gravitational force acting on the sphere to the electric force acting on it due to the electric field.
The gravitational force (weight) can be calculated using the formula Fg = m x g, where m is the mass of the sphere and g is the acceleration due to gravity (9.81 m/s2). For a 9.2 g sphere, the weight is:
Fg = 0.0092 kg * 9.81 m/s2 = 0.090252 N.
Next, the electric force on a charge q in an electric field E is given by the formula Fe = qE. To balance the weight, the electric force must be equal in magnitude:
Fe = Fg => qE = 0.090252 N.
Solving for E when the charge q is -5.2 nC (or -5.2 x 10-9 C) gives us:
E = 0.090252 N / -5.2 x 10-9 C ≈ -17.36 x 106 N/C.
The negative sign indicates the direction of the electric field is opposite to the charge's direction, but since we're only asked for the magnitude, the strength of the electric field would be 17.36 x 106 N/C.