A foam ball of a mass of 0.150 g carries a charge of -2.00 nC. The ball is in a uniform electric field, and is suspended against the force of gravity. What are the magnitude and direction of the electric field?
M g = E Q
Solve for the field magnitude E. You will need the value of g, which I am sure you already know.
The direction of the E-field is down, so that an upward force is applied to a negative charge.
A foam ball of mass 0.150 g carries a charge of -2.00 nC. The ball is placed inside a uniform
electric field, and is suspended against the force of gravity. What are the magnitude and
direction of the electric field?
A) 573 kN/C down
B) 573 kN/C up
C) 735 kN/C down
D) 735 kN/C up
To find the magnitude and direction of the electric field, we can use the equation for the electric force experienced by a charged particle in an electric field:
Electric force (F) = charge (q) * electric field (E)
In this case, the ball is suspended against the force of gravity, meaning that the electric force is equal in magnitude and opposite in direction to the gravitational force acting on the ball.
The gravitational force is given by:
Gravitational force (Fg) = mass (m) * acceleration due to gravity (g)
The ball is in equilibrium, so the electric force and gravitational force are equal in magnitude:
F = Fg
Using the equations for electric force and gravitational force, we can set up the following equation:
q * E = m * g
Let's plug in the values:
q = -2.00 nC = -2.00 * 10^-9 C
m = 0.150 g = 0.150 * 10^-3 kg
g = 9.8 m/s^2
Plug in these values and solve for the electric field (E):
(-2.00 * 10^-9 C) * E = (0.150 * 10^-3 kg) * (9.8 m/s^2)
E = [(0.150 * 10^-3 kg) * (9.8 m/s^2)] / (-2.00 * 10^-9 C)
E ≈ -7.35 * 10^5 N/C
So, the magnitude of the electric field is approximately 7.35 * 10^5 N/C, and it is directed opposite to the gravitational force.
To find the magnitude and direction of the electric field, we can use the formula:
Electric Force = Charge x Electric Field
The electric force experienced by the foam ball is equal to the force due to gravity, as it is suspended against the force of gravity. Since the ball is in equilibrium, these forces need to be equal in magnitude but opposite in direction.
The force due to gravity experienced by the ball can be calculated using the formula:
Force due to gravity = Mass x Gravity
Where:
Mass = 0.150 g (convert to kg by dividing by 1000)
Gravity = 9.8 m/s^2
Now, we can equate the forces and solve for the electric field:
Force due to gravity = Electric Force
Mass x Gravity = Charge x Electric Field
Substituting the given values:
(0.150 g / 1000 kg/g) x 9.8 m/s^2 = (-2.00 nC) x Electric Field
Solving for Electric Field:
Electric Field = (0.150 kg x 9.8 m/s^2) / (-2.00 x 10^-9 C)
Let's calculate the magnitude and direction of the electric field using this formula.