A proton is released from rest in a uniform electric field...

Key Concepts

Uniform Electric Field

A uniform electric field is one in which the field intensity (magnitude and direction) remains constant throughout the region. In such a field, any charge placed within experiences a constant force, making the analysis of motion predictable and straightforward.

Force on a Charged Particle

A charged particle in an electric field experiences a force calculated by F = qE, where q is the charge and E is the electric field. This relationship is central to understanding the acceleration of charged particles in various fields, as it directly connects the properties of the particle with the external field.

Work-Energy Principle

The work-energy principle states that the work done on an object by a force is equal to the change in its kinetic energy. In the context of electrically accelerated particles, the work done by the electric force (qE multiplied by displacement) converts into the kinetic energy of the particle, thereby determining its speed after traveling a certain distance.

Kinematics in Uniform Acceleration

When a particle starts from rest and experiences constant acceleration, as is the case in a uniform electric field, kinematic equations can be used to relate displacement, acceleration, and final velocity. This concept is essential for predicting the speed of the particle after it has been accelerated over a known distance.

Transcript

00:01 Question 73 states that a proton is released from rest in a uniform electric field of magnitude 2 .18 times 10 to the 5 nons per kulo.

00:15 Find the speed of the proton after it has left, after it has traveled both 1 centimeter and 10 centimeters.

00:24 Okay, so this is a move just given.

00:26 A couple of things here.

00:27 It does tell us that it starts from rest.

00:29 If you want to find the final velocity at a different time point, we need to think of how we can approach this question from a kinematics perspective.

00:39 So in a kinematics, if we're given a final velocity, or at least we're looking for final velocity, we're given an initial velocity, and we're given a distance.

00:48 The appropriate equation that would combine all three of these would be, because it starts from zero and goes to a higher velocity, we need to use the kinematic equation that our final velocity equals our initial velocity squared, plus 2 times ad.

01:12 Again, if we're starting from rest, this term goes to zero, but we don't have an acceleration term as of yet.

01:21 Right, so we know that this proton is released in an electric field, so we know that the force that this charge this proton would experience has to be equal to ma because it is in motion, because again, it's an electric field that has to equal q times e.

01:39 So we can determine that our acceleration that this particle undergoes is the charge, it has times an electric field over its mass, but while i mean, we're only given an electric field, the charge of our proton is known, as well as the mass of the proton.

01:54 So we can use these values in our solution.

01:57 So starting from this equation, we can rearrange it to solve for acceleration, but we're going to leave it as acceleration as such and just solve for final velocity.

02:09 So our final velocity is equivalent to times 2 times d times acceleration, qe over m, and this whole term is squared because v was squared initially...

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