A free proton and a free electron are placed in uniform feild which of...
Introduction
When a free proton and a free electron are placed in a uniform field, they experience different forces and accelerations due to their opposite charges. In this explanation, we will explore why the proton experiences a greater force and acceleration compared to the electron.
Force on a Charged Particle
The force experienced by a charged particle in a uniform electric field can be calculated using the equation F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength. Both the proton and the electron have the same magnitude of charge, which is e, the elementary charge (1.6 x 10^-19 C).
Force and Acceleration in the Electric Field
The force experienced by a charged particle in a uniform electric field causes it to accelerate. The acceleration can be calculated using the equation a = F/m, where a is the acceleration, F is the force, and m is the mass of the particle. The mass of a proton is approximately 1.67 x 10^-27 kg, while the mass of an electron is approximately 9.11 x 10^-31 kg.
Explanation
1. Force: The magnitude of the force experienced by a charged particle in a uniform electric field is directly proportional to the charge of the particle. Since both the proton and the electron have the same magnitude of charge, they experience the same magnitude of force.
2. Acceleration: The acceleration of a charged particle in a uniform electric field is inversely proportional to its mass. Since the proton has a much larger mass than the electron, it experiences a smaller acceleration compared to the electron.
3. Comparison: Although the proton experiences a smaller acceleration, it still experiences a greater force compared to the electron due to its larger mass. The electron, on the other hand, experiences a greater acceleration but a smaller force due to its smaller mass.
Conclusion
In conclusion, when a free proton and a free electron are placed in a uniform electric field, the proton experiences a greater force but a smaller acceleration compared to the electron. This is due to the proton's larger mass, which results in a smaller acceleration but a greater force according to the equations F = qE and a = F/m.