Final answer:
The magnitude electric field required to balance the weight of a particle with a charge of 4 C and a mass of 5 g is 0.01225 N/C, directed upward.
Step-by-step explanation:
The question asks for the magnitude of the electric field that would exactly balance the weight of a particle with a charge of 4 C and a mass of 5 g. To find this, we need to equate the electrical force exerted on the charged particle by the electric field to the gravitational force acting on the mass of the particle due to gravity. The equation for the electric force (Fe) is Fe = qE, where q is the charge and E is the electric field.
The gravitational force (Fg) on the particle is Fg = mg, where m is the mass and g is the acceleration due to gravity, which is approximately 9.8 m/s2. Setting these equal to each other, we get: qE = mg. To find the electric field, we plug in the values for q, m, and g, thus: 4 C × E = 0.005 kg × 9.8 m/s2. From this, we solve for E, resulting in an electric field required to balance the gravitational force of: E = (0.005 kg × 9.8 m/s2) / 4 C = 0.01225 N/C directed upward.