I would like logic on how to solve this problem.
A styrofoam ball covered with a conducting paint has a mass of 5.0 x 10 ^-3 kg and has a charge of 4.0 microcoulombs. What electric field directed upward will balance the weight of the ball?
A styrofoam ball covered with a conducting paint has a mass of 5.0 x 10 ^-3 kg and has a charge of 4.0 microcoulombs. What electric field directed upward will balance the weight of the ball?
Set the Coulomb force E*Q equal to the gravity force (weight), M g. Assume the charge is uniformly distributed around the surface. (This would be necessary since the surface is conducting). The sphere will behave as if it were a point charge of 4.0 microCoulombs at the center of the sphere.
Sorry (impatient) and Thank you for your time.
So is
E=/F/ divide by /q/
To solve this problem, we need to understand the principles of electrostatics and the forces acting on the styrofoam ball.
1. Identify the known values:
- Mass of the styrofoam ball: 5.0 x 10^-3 kg
- Charge of the ball: 4.0 microcoulombs
2. Understand the forces acting on the ball:
- The ball experiences two main forces: weight (due to gravity) and the electrostatic force (due to its charge and the electric field).
- The weight force is given by: F_weight = m * g, where m is the mass and g is the acceleration due to gravity (approximated as 9.8 m/s^2).
- The electrostatic force is given by: F_electrostatic = q * E, where q is the charge and E is the electric field.
3. Since the ball is in equilibrium (the forces are balanced), the electrostatic force must be equal and opposite to the weight force.
- Therefore, F_electrostatic = F_weight
4. Set up the equations:
- F_weight = m * g
- F_electrostatic = q * E
5. Equate the two forces and solve for the electric field (E):
- q * E = m * g
- E = (m * g) / q
6. Substitute the known values:
- m = 5.0 x 10^-3 kg
- g = 9.8 m/s^2
- q = 4.0 x 10^-6 C
E = (5.0 x 10^-3 kg * 9.8 m/s^2) / (4.0 x 10^-6 C)
7. Calculate the electric field:
- E = 1.225 x 10^3 N/C
Therefore, an electric field of 1.225 x 10^3 N/C directed upward will balance the weight of the styrofoam ball.