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Motion of a Charged Particle in a Uniform Field

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

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Motion of a Charged Particle in a Uniform Field

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  1. Motion of a Charged Particle in a Uniform Field Physics 12 Adv

  2. 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

  3. 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

  4. 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

  5. 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

  6. EOMs

  7. 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

  8. 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.

  9. 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

  10. 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

  11. How can we calculate centripetal acceleration?

  12. 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

  13. 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

  14. Radius of Curvature

  15. 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?

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