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Download Lesson 17 - Motion of a Charged Particle in a Uniform Field
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Motion of a Charged Particle in a Uniform Field Physics 12 Adv Charged Particle placed in an EField 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 qE a m Charged Particle moving in an EField 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 v (t ) at v0 2 at d (t ) v0t d 0 2 vx (t ) a x t v0 x 2 axt v0 x t d 0 x d x (t ) 2 v y (t ) a y t v0 y 2 a yt v0 y t d 0 y d y (t ) 2 Charged Particle moving in an EField 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 BField 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 v r v d vt r vt vt v r v 2 v v r t v2 ac r 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 F ma 2 v ac r 2 mv Fc r Charged Particle moving in an BField 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 mv 2 Fc r F qv B F qvB mv 2 qvB r mv r qB 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?