An object with a net charge of 21 µC is placed in a uniform electric field of 590 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 can use the following equation:
Electric force = Gravitational force
The electric force is given by the equation:
Electric force = charge ⋅ electric field
The gravitational force is given by the equation:
Gravitational force = mass ⋅ gravity
Since the object is "floating" in the electric field, the electric force is equal in magnitude to the gravitational force. Thus, we can equate the two equations:
charge ⋅ electric field = mass ⋅ gravity
Now, let's substitute the given values into the equation:
21 µC ⋅ 590 N/C = mass ⋅ 9.8 m/s^2
First, let's convert the charge from microcoulombs to coulombs:
21 µC = 21 × 10^-6 C
Now, let's rearrange the equation to solve for mass:
mass = (charge ⋅ electric field) / gravity
mass = (21 × 10^-6 C ⋅ 590 N/C) / 9.8 m/s^2
mass ≈ 1.27 × 10^-3 kg
Therefore, the mass of the object is approximately 1.27 × 10^-3 kg.
To find the mass of the object, we need to use the concept of electric force and gravitational force.
First, let's find the electric force acting on the object. The electric force (F_electric) can be calculated using the equation:
F_electric = q * E
where q is the net charge of the object and E is the electric field strength.
Given:
Net charge (q) = 21 µC = 21 * 10^(-6) C
Electric field strength (E) = 590 N/C
Substituting these values into the equation, we get:
F_electric = (21 * 10^(-6) C) * (590 N/C)
F_electric = 1.239 * 10^(-3) N
Next, we need to determine the gravitational force acting on the object. The gravitational force (F_gravity) can be calculated using the equation:
F_gravity = m * g
where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the object is "floating" in the electric field, the electric force and gravitational force are equal:
F_electric = F_gravity
1.239 * 10^(-3) N = m * 9.8 m/s^2
Solving for the mass (m):
m = (1.239 * 10^(-3) N) / (9.8 m/s^2)
m ≈ 0.126 kg
Therefore, the mass of the object is approximately 0.126 kg.