An object with a net charge of 20 µC is placed in a uniform electric field of 627 N/C, directed vertically. What is the mass of the object if it floats in the electric field?
To determine the mass of the object, we need to use the concept of electric force and gravitational force.
1. Electric force (Fe): It is given that the object has a net charge of 20 µC and is placed in a uniform electric field of 627 N/C. The electric force experienced by the object can be calculated using the equation:
Fe = q * E
Where Fe is the electric force, q is the charge, and E is the electric field strength.
Plugging in the values:
Fe = (20 × 10^-6 C) * (627 N/C)
Fe = 0.01254 N
2. Gravitational force (Fg): The object is floating in the electric field, which means the gravitational force is balanced by the electric force. Therefore, the gravitational force acting on the object is equal to the electric force.
Fg = Fe = 0.01254 N
3. Weight (W): The weight of an object is given by the equation:
W = m * g
Where W is the weight, m is the mass, and g is the acceleration due to gravity.
In this case, since the object is floating, the weight is balanced by the electric force, so we can equate the two:
W = Fe = 0.01254 N
4. Rearranging the equation for weight, we can solve for mass:
m = W / g
Plugging in the given value of g (approximately 9.8 m/s^2):
m = 0.01254 N / 9.8 m/s^2
m = 0.00128 kg
Therefore, the mass of the object is approximately 0.00128 kg.