An object with a net charge of 35 µC is placed in a uniform electric field of 643 N/C, directed vertically. What is the mass of the object if it floats in the electric field?

A sphere with a net charge of 10 µC is placed in a uniform electric field of 210 N/C directed vertically. What is the mass of this object if it “floats” in the field?

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To find the mass of the object that floats in the electric field, we need to use the concept of electrostatic force and gravitational force balance.

First, we know that the electrostatic force (Fe) acting on an object in an electric field is given by the equation:

Fe = qE

where q is the charge of the object and E is the electric field strength.

In this case, the charge of the object (q) is given as 35 µC (35 × 10^-6 C), and the electric field strength (E) is given as 643 N/C.

So, we can calculate the electrostatic force as:

Fe = (35 × 10^-6 C) × (643 N/C)

Next, we need to consider the gravitational force (Fg) acting on the object, which is given by the equation:

Fg = mg

where m is the mass of the object and g is the acceleration due to gravity.

Since the object floats in the electric field, the electrostatic force must balance the gravitational force. Therefore, we can equate the two forces:

Fe = Fg

Substituting the equations for Fe and Fg:

(35 × 10^-6 C) × (643 N/C) = m × g

To find the mass (m), we need the value of acceleration due to gravity (g). On Earth, the standard value is approximately 9.8 m/s^2. However, in this question, the direction of the electric field is vertically, so we need to consider the acceleration due to gravity in the vertical direction.

In this case, g will be the component of the acceleration due to gravity that is in the vertical direction. Assuming that the electric field is also directed vertically, the net force on the object will be zero.

So, we can write:

Fe = Fg

(35 × 10^-6 C) × (643 N/C) = m × g

Simplifying the equation:

(35 × 10^-6) × (643 N/C) = m × g

Solving for m:

m = (35 × 10^-6) × (643 N/C) / g

Substituting the value of g (approximately 9.8 m/s^2):

m = (35 × 10^-6) × (643 N/C) / 9.8 m/s^2

m ≈ 0.002297 kg

Therefore, the mass of the object is approximately 0.002297 kg.

Wouldn't the electrical force= gravity?