An object having a net charge of -24 Micro C is placed in a uniform electric field of 610 N/C directly vertically. What is the mass of the object if it floats in the field?

To determine the mass of the object, we can use the concept of electric force and gravitational force.

Step 1: Calculate the electric force acting on the object. The electric force (F_electric) can be calculated using the formula: F_electric = q * E where q is the charge of the object and E is the electric field strength.

Given: q = -24 μC (microcoulombs) E = 610 N/C

Converting the charge to coulombs: q = -24 μC = -24 * 10^(-6) C = -2.4 * 10^(-5) C

Substituting the values into the formula: F_electric = (-2.4 * 10^(-5) C) * (610 N/C) F_electric = -14.64 * 10^(-3) N

Step 2: Calculate the gravitational force acting on the object. The gravitational force (F_gravity) can be calculated using the formula: F_gravity = m * g where m is the mass of the object and g is the acceleration due to gravity.

Given: g = 9.8 m/s^2 (approximate value on Earth)

Substituting the values into the formula: F_gravity = m * 9.8

Step 3: Equate the electric force and gravitational force. Since the object is floating, the electric force and gravitational force must be equal: F_electric = F_gravity

Therefore, we can equate the two equations: -14.64 * 10^(-3) N = m * 9.8

Step 4: Solve for the mass of the object. Rearranging the equation to solve for m: m = (-14.64 * 10^(-3) N) / 9.8

Calculating the value: m ≈ -1.49 * 10^(-3) kg

Note: The negative sign indicates that the object has a negative charge and is likely made of a material with a lower density than the surrounding medium, causing it to float.

Therefore, the mass of the object is approximately -1.49 * 10^(-3) kg.