Understanding the Concepts
* Electric Force: A charged particle experiences a force in an electric field. The magnitude of this force is given by:
F = qE
where:
* F is the force
* q is the charge of the particle
* E is the strength of the electric field
* Newton's Second Law: This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:
a = F/m
where:
* a is the acceleration
* F is the net force
* m is the mass
Derivation
1. Force on Electron: The force on an electron (charge -e) in an electric field is:
F_electron = -eE
2. Force on Proton: The force on a proton (charge +e) in the same electric field is:
F_proton = +eE
3. Acceleration of Electron: Using Newton's Second Law:
a_electron = F_electron / m_electron = (-eE) / m_electron
4. Acceleration of Proton: Using Newton's Second Law:
a_proton = F_proton / m_proton = (eE) / m_proton
5. Ratio of Accelerations: Divide the acceleration of the electron by the acceleration of the proton:
(a_electron) / (a_proton) = [(-eE) / m_electron] / [(eE) / m_proton]
Simplifying, we get:
(a_electron) / (a_proton) = - (m_proton / m_electron)
Result
The ratio of the acceleration of the electron to the acceleration of the proton is equal to the negative ratio of their masses. Since the proton is much heavier than the electron, the electron will experience a much larger acceleration in the same electric field.
Important Note: The negative sign indicates that the electron and proton accelerate in opposite directions due to their opposite charges.
