A particle with a charge of +4.20 nC is in a uniform electric field E⃗ directed to the left. It

A particle with a charge of +4.20 nC is in a uniform...

A particle with a charge of $+4.20 \mathrm{nC}$ is in a uniform electric field $\vec{\boldsymbol{E}}$ directed to the left. It is released from rest and moves to the left; after it has moved $6.00 \mathrm{cm},$ its kinetic energy is found to be $+1.50 \times 10^{-6} \mathrm{J}$ (a) What work was done by the electric force? (b) What is the potential of the starting point with respect to the endpoint? (c) What is the magnitude of $\vec{E} ?$

Key Concepts

Uniform Electric Field

A uniform electric field is one in which the magnitude and direction of the electric field vector remain constant at every point in space. This concept is essential because it leads directly to a constant force on a charged particle regardless of its location in the field, which simplifies the calculations of work and potential differences. In contexts of charged particle motion, a uniform electric field provides a predictable and linear relationship between the spatial displacement and the resulting potential difference.

Work-Energy Theorem

The work?energy theorem states that the net work done on an object is equal to its change in kinetic energy. In the case of a charged particle moving in an electric field, this theorem allows us to relate the work done by the electric force to the gain or loss in the particle’s kinetic energy. This concept is fundamental in physics as it links the force applied over a distance to the energy transformation that occurs as a result of that force.

Electric Potential Difference

Electric potential difference is defined as the work done per unit charge in moving a test charge between two points in an electric field. It represents the energy change of the charge due to the field, and is closely linked to the field itself through the relation ?V = -E·d, where d is the displacement in the direction of the field. Understanding this relationship is crucial for analyzing energy transitions in charged particle dynamics, particularly when converting electrical potential energy into kinetic energy.

Transcript

00:01 In this question, we have a positive electric charge that is placed into a uniform electric field.

00:06 And it moves by a certain distance.

00:09 And the electric field is pointing to the left.

00:12 And this positive charge moves under the electric field, so we will expect that it will also move to the left, because positive charges move along the electric field lines.

00:23 And it's released from rest, and then because of the electric field, it accelerates to have a a certain kinetic energy, ke of 1 .5 times 10 to the negative 6 gel, after it has moved d equals 6 .00 cm.

00:43 And the electric charge is 0 .420 dynodon.

00:52 So part a, it asks us, what is the potential of the starting point with respect to the endpoint? and in order to, part a asks us what work is done by the electric force.

01:06 So whatever energy is increased by the positive charge is because of the electric field.

01:14 So here the increase of energy is shown in the form of kinetic energy.

01:19 So this much kinetic energy is resulted from the work down by the electric force.

01:28 So because of that we can just say work equals kinetic energy.

01:34 Equals 1 .5 times 10 to the negative 6.

01:37 John.

01:38 So if we want to be really precise, this is actually the difference of kinetic energy, which should be the kinetic energy at the endpoint, minus the kinetic energy at the initial point.

01:51 But here, i'm just writing it as a kinetic energy because it's starting from rest, so we know the initial kinetic energy is just zero.

02:00 So part you ask us, what is the potential of the starting point with respect to the endpoint? so it's asking us what is the potential difference...

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