What must the charge (sign and magnitude) of a particle of mass 1.47g be for it to remain stationary when placed in a downward-directed electric field of magnitude 690N/C ?
Use 9.81m/s2 for the magnitude of the acceleration due to gravity.
PART B
What is the magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight?
Use 1.67×10−27kg for the mass of a proton, 1.60×10−19C for the magnitude of the charge on an electron, and 9.81m/s2 for the magnitude of the acceleration due to gravity.
To solve these problems, we need to use the equations that relate the electric force, gravitational force, and the charge of a particle. Here's how you can find the answers:
PART A:
To find the charge of the particle, we need to determine the force of gravity acting on it and equate it to the electric force.
1. Calculate the force of gravity using the formula:
Force_gravity = mass * acceleration_due_to_gravity
Plugging in the given values:
Force_gravity = 1.47g * 9.81m/s²
2. The electric force can be calculated using the formula:
Electric_force = charge * electric_field
Plugging in the given values:
Electric_force = charge * 690N/C
3. Set the force of gravity equal to the electric force:
Force_gravity = Electric_force
4. Substitute the calculated values:
1.47g * 9.81m/s² = charge * 690N/C
5. Solve for the charge:
charge = (1.47g * 9.81m/s²) / 690N/C
Based on the calculation above, you can find the charge (sign and magnitude) that will keep the particle stationary.
PART B:
To find the magnitude of the electric field, we need to equate the force of gravity acting on the proton to the electric force.
1. Calculate the force of gravity on the proton using the formula:
Force_gravity = mass * acceleration_due_to_gravity
Plugging in the given values:
Force_gravity = (1.67×10−27kg) * (9.81m/s²)
2. The electric force experienced by the proton can be calculated using Coulomb's law:
Electric_force = (charge_proton * charge_electron) / distance²
Since we want the electric force to be equal to the force of gravity, we can set them equal to each other:
Force_gravity = Electric_force
3. Substitute the known values:
(1.67×10−27kg * 9.81m/s²) = (charge_proton * 1.60×10−19C) / distance²
4. Rearrange the equation to solve for the electric field magnitude:
Electric_field = (charge_proton * 1.60×10−19C) / (distance² * Force_gravity)
Again, you can plug in the given values to find the magnitude of the electric field in which the electric force on the proton is equal to its weight.