Motion of a Charged Particle in a Uniform Field

Physics 12 Adv

Charged Particle placed in an E-Field When a charged

particle is placed in an electric field, it experiences a force based on the field strength and charge

Determine an equation that solves for acceleration of a particle in terms of q, m and E m

Eqa

Charged Particle moving in an E-Field When a charged

particle is moving in an electric field, it will experience an acceleration parallel to the electric field

This requires that we treat the motion in two dimensions using trigonometry

Motion in 2D

Previously we have constrained objects to move in one dimension

We are now going to remove that constraint and investigate the motion of a charged particle in a uniform electric field, where the particle is free to move in both the x and y direction

Charged Particle Motion with an Initial Velocity When we consider a charged particle

moving in an electric field, we will consider either the x or y axis to be in the direction of the electric field

We can then consider the velocity using vector components and write equations of motion to describe the charged particle

EOMs

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Charged Particle moving in an E-Field An electron, moving

with an initial velocity enters an electric field as shown in the diagram at the right and will follow a parabolic path as a result of the e-field

We can solve this problem through the use the 2D EOM’s

Problem

A cathode ray tube is created using a potential difference of 5.0kV between A and B. An electron is emitted from A and accelerated toward B where A and B are separated by 9.5cm. After passing B, the electron travels at a constant velocity until it enters the electric field created by C and D. C and D are separated by 2.5cm and the plates are 5.0cm long; what is the maximum voltage that can be applied to the plates so that the electron does not strike either plate.

Charged Particle placed in a B-Field When a charged

particle is placed in a magnetic field, it experiences a force based on the cross product of its velocity and the magnetic field intensity

Therefore, a charged particle experiences no force if it is not moving

Circular Motion

When a charged particle is moving in a magnetic field, it always experiences a force that is at right angles to the velocity

This results in a change in the direction of the velocity but not its magnitude

As a result, this force will provide a centripetal acceleration towards the centre of the circular path

How can we calculate centripetal acceleration?

r

va

t

v

r

v

v

v

r

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tvr

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r

r

c

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2

Centripetal Force

Like the centripetal acceleration, the centripetal force is always directed towards the centre of the circle

The centripetal force can be calculated using Newton’s Second Law of Motion r

mvF

r

va

amF

c

c

2

2

Charged Particle moving in an B-Field A charged particle,

moving with an initial velocity enters a magnetic field as shown in the diagram at the right and will follow a circular path as a result of the b-field

We can solve this problem through the use the centripetal motion

Radius of Curvature

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mvr

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mv

qvBF

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r

mvFc

2

2

Problem

An electron is accelerated through a potential difference of 2.5kV before entering a uniform magnetic field of strength 0.50T. What is the radius of curvature of the electron?