If the electric field between plates (A) is 1.0 ×10^3 N / C in the +x -direction, what is the ho

If the electric field between plates (A) is 1.0 ×10^3 N / C...

If the electric field between plates (A) is $1.0 \times 10^{3} \mathrm{N} / \mathrm{C}$ in the $+x$ -direction, what is the horizontal deflection $(\Delta x)$ of the beam as it exits the region between plates (A)?

Key Concepts

Electric Field

An electric field is a region of space where a charged particle experiences a force. The magnitude and direction of the force on a particle are determined by the electric field and the particle's charge, with the force given by F = qE. This concept is fundamental for understanding how charged particles behave in various environments, bridging the gap between electromagnetism and mechanics.

Force on a Charged Particle

The force acting on a charged particle in an electric field arises directly from the interaction between the field and the charge it carries. This electrostatic force, calculated as the product of the charge and the electric field, causes the particle to accelerate, with the acceleration determined by Newton's second law. This principle is essential for analyzing and predicting the motion of charged particles in fields.

Uniform Acceleration Kinematics

When a constant force, such as that from a uniform electric field, acts on a particle, the particle undergoes uniform acceleration. Classical kinematics provides the framework to calculate displacement, velocity, and time of motion using equations that assume constant acceleration. This approach is key to determining the trajectory and deflection of moving particles under the influence of consistent forces.

Transcript

00:01 High in the given problem, the set of plates which is marked as a is vertical.

00:12 Here these are the plates, vertical plates like this.

00:24 The plates are square sized.

00:30 There is a z -axis, the direction along z -axis.

00:36 This is horizontal.

00:37 Then this plate the inner one that is positively charged the outer plate this one this one is negatively charged so if this is supposed to be positive x -axis here this is positive z -axis then electric field between the plates is along positive x -axis directed like this now the electron beam passes through the plates moving along z -axis so due to this electric field which is directed along positive x -axis this electron beam will be deflected towards the positively charged plates like this.

01:41 So we have to find this deflection delta x and that deflection will be in the direction of negative x -axis definitely because the electrons will be deflected towards the positively charged plates.

02:02 Now the speed of electrons in the direction of x x, let it be v i, the initial speed along z -axis, v iz, is given as 8 .4 into 10 dash 6 meter per second.

02:25 The gap between the plates, the total gap, let it be is given as 1 .50 centimeter the size of these square plates is given as 2 .50 centimeter hence we can say distance traveled by the electrons along the x -axis within the electric field and let it be z is equal to 2 .50 centimeter the magnitude of electric field is e is equal to 1 .0 into 10 reached to 3 newton per coulon now as the electrons will enter into this electric field they will start experiencing an electrostatic force f e, that will be given by e into e, the product of electronic charge with the electric field.

04:08 And using newton's second law of motion, that will be equal to m .a .x.

04:13 Here, this ax will be the acceleration in the motion of electron along x -axis...

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