I'm stumped:
2 charges, Q1 and Q2, equal magnitude, but different signs (not assigned) lie on a line, x axis, a known distance apart.
Segment pq lies centrally on the line, distance apart is known.
An electron is released at p from rest, and passes q at a given time later. The field at pq is constant.
My job is to find the size and sign of Q1 and Q2 on this info.
I believe i can calculate the electrical force on the electron, but where next? Thanks
I don't understand how the field is constant along pq. I am certain the force will vary with position.
Sorry, the field is said to be constant around the central segment pq, which is only 10 cm long.
To find the size and sign of charges Q1 and Q2, you can follow these steps:
1. Determine the electrical force on the electron:
- The electrical force experienced by the electron between points p and q can be calculated using Coulomb's Law: F = (k * |Q1| * |Q2|) / r^2, where k is the electrostatic constant, |Q1| and |Q2| are the magnitudes of the charges, and r is the distance between the charges.
- Since the electron is released from rest, the electrical force is equal to the net force acting on the electron.
2. Calculate the acceleration of the electron:
- Use Newton's second law, F = m * a, where m is the mass of the electron, and a is its acceleration.
- Since the mass of the electron is known, you can solve for the acceleration.
3. Determine the time it takes for the electron to travel from p to q:
- Assuming the motion is along a straight line and the acceleration is constant, you can use the kinematic equation: d = v0 * t + (1/2) * a * t^2, where d is the distance between points p and q, v0 is the initial velocity, t is the time taken, and a is the acceleration.
- The initial velocity v0 is zero since the electron is released from rest.
- Rearrange the equation to solve for t.
4. Use the time obtained to determine the net force on the electron through the electrical force equation.
5. Compare the magnitude of the electrical force to net force (including the direction) to determine the relative signs of Q1 and Q2:
- If the electrical force and net force have the same direction, then the charges have the same sign.
- If they have opposite directions, then the charges have opposite signs.
Once you have the relative signs of Q1 and Q2, you can use their magnitudes to find their individual values by comparing them to the distance between the charges and solving for the unknowns.