A negatively charged particle of mass 5.00 ×10^-19 kg is moving with a speed of 35.0 m / s when

A negatively charged particle of mass 5.00 ×10^-19 kg is...

A negatively charged particle of mass $5.00 \times 10^{-19} \mathrm{kg}$ is moving with a speed of $35.0 \mathrm{m} / \mathrm{s}$ when it enters the region between two parallel capacitor plates. The initial velocity of the charge is parallel to the plate surfaces and in the positive $x$ -direction. The plates are square with a side of $1.00 \mathrm{cm},$ and the voltage across the plates is $3.00 \mathrm{V}$. If the particle is initially $1.00 \mathrm{mm}$ from both plates and it just barely clears the positive plate after traveling $1.00 \mathrm{cm}$ through the region between the plates, how many excess electrons are on the particle? Ignore gravitational and edge effects.

Key Concepts

Electric Field

The electric field is a vector quantity representing the force per unit charge at any point in space. In the context of a parallel plate capacitor, the field is uniform and its magnitude is determined by the voltage difference between the plates divided by their separation. Understanding this concept is crucial for analyzing how charged particles behave in such fields.

Electric Potential Difference

Voltage or electric potential difference is the work done per unit charge to move a charge between two points. In capacitor problems, the voltage across the plates determines the magnitude of the electric field, influencing the force experienced by a charged particle moving between the plates.

Force on a Charged Particle

A charged particle in an electric field experiences a force given by F = qE, where q is the charge of the particle and E is the electric field. This concept explains how positive and negative charges are accelerated in opposite directions by the field and is essential for determining the particle's motion.

Kinematics with Constant Acceleration

When a particle experiences a constant force, it undergoes constant acceleration. The kinematic equations link displacement, velocity, acceleration, and time, and are used to predict the particle's trajectory. This concept is important when analyzing the deflection of a charged particle subjected to a uniform electric field.

Charge Quantization

Electric charge is quantized in units of the elementary charge, meaning that any charged object has a charge that is an integer multiple of the charge of a single electron. This principle is used to determine the number of extra electrons on a particle once its total charge is known.

Transcript

00:01 Hi, in the given problem there are two metallic parallel charged plates, the square shaped charge plates, mass of the negative charged particle which is allowed to enter into this electric field provided between these two plates.

00:38 Here, this is the charged particle which will be entering perpendicular to the electric field the mass of this charge particle is given as 5 .00 into 10 dash per minus 19 kilogram its initial speed along x -axis is given to be vx is equal to 35 .0 meter per second the side length of the plate is given to be l is equal to 1 .00 cm or we can say this is 1 .00 into 10 dash to power minus 2 meter this is the side length and that will be the expansion of electric field also potential difference applied between the plates is given as 3 .00 volt and as the gas gap between the plates is 2 .00 millimeter.

01:59 So it is said that when this charged particle will be deviated towards the positively charged plate and when it will be coming out of the electric field it will be just touching the edge of this lower positively charged plate.

02:19 Hence, we can say the vertical deflection delta y, vertical deflection made by the charged particle within the electric field is given as delta y is equal to 1 .00 millimetre as the negatively charged particle is deviating towards the lower plate means this lower plate should be positively charged and the upper plate is negatively charged.

03:19 So the direction of electric field here is upward between the plates from positive plate to negative plate and the field is uniform.

03:32 Now, this distance vertical displacement can also be given as 1 .00 into 10 dash par minus 3 meter.

03:46 Now as the charge particle does not experience any force along x -axis, the force experienced by the charge particle will be only along vertical, means along y -axis.

03:59 So, motion of the charge particle will remain uniform along x, x, is hence time taken by the charge particle within this electric field will be given by t is equal to distance upon speed, distance is equal to the length of the plate, side of the plate, speed vx...

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