Motion Of Charges In The Presence of Electric and Magnetic Fields

Topic: JJ Thomson’s Experiment

• Introduction to JJ Thomson’s Experiment
• Aim of the Experiment
• Apparatus used in the Experiment:
  • Cathode Rays Tube (CRT)
  • Magnetic field generator
  • Electric field generator
• Working Principle of the Experiment:
  • The electric and magnetic fields applied on the cathode rays
  • Deflection of cathode rays based on the strength and direction of fields
  • Determination of charge-to-mass ratio of the electron
• Equations used in the Experiment:
  • F = q(E + v × B)
  • F = qE
  • F = qvB
• Significance of JJ Thomson’s Experiment

Principle of Superposition of Electric Fields

• When multiple electric fields act on a charge, the resultant electric field is the vector sum of the individual electric fields.
• The electric field at a point is given by the equation: $\vec{E}_{\text{net}} = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + … + \vec{E}_n$
• The direction of the resultant electric field is determined by the vector sum of the individual electric fields.

Force on a Charged Particle in an Electric Field

• An electric field exerts a force on a charged particle.
• The force experienced by a charged particle in an electric field is given by the equation: $\vec{F} = q\vec{E}$
• Here, $\vec{F}$ is the force, $q$ is the charge of the particle, and $\vec{E}$ is the electric field.
• The direction of the force is determined by the vector nature of the electric field and the charge of the particle.

Motion of Charged Particles in a Magnetic Field

• A magnetic field exerts a force on a moving charged particle.
• The force experienced by a charged particle moving in a magnetic field is given by the equation: $\vec{F} = q\vec{v} \times \vec{B}$
• Here, $\vec{F}$ is the force, $q$ is the charge of the particle, $\vec{v}$ is the velocity of the particle, and $\vec{B}$ is the magnetic field.
• The direction of the force is determined by the cross product of the velocity and the magnetic field.

Motion of Charged Particles in Electric and Magnetic Fields

• When both electric and magnetic fields are present, a charged particle experiences a combined force due to both fields.
• The net force experienced by a charged particle in electric and magnetic fields is given by the equation: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$
• The motion of charged particles in electric and magnetic fields can be determined by analyzing the net force acting on the particle.
• The direction and magnitude of the net force depend on the strength and orientation of the electric and magnetic fields.

Motion of Charged Particles in Opposing Electric and Magnetic Fields

• If the electric field and magnetic field are in opposite directions, the net force on a charged particle depends on the velocity of the particle.
• If the velocity of the charged particle is zero, the net force experienced by the particle is only due to the electric field: $\vec{F} = q\vec{E}$
• If the velocity of the charged particle is non-zero, the net force experienced by the particle is due to the electric field and the cross product of velocity and the magnetic field: $\vec{F} = q\vec{E} + q\vec{v} \times \vec{B}$

Motion of Charged Particles in Perpendicular Electric and Magnetic Fields

• If the electric field and magnetic field are perpendicular to each other, the net force on a charged particle is always perpendicular to its velocity.
• The charged particle moves in a circular path due to the balance between the electric and magnetic forces.
• The radius of the circular path can be calculated using the equation: $r = \frac{mv}{|q|B}$, where $m$ is the mass of the particle, $v$ is its velocity, $|q|$ is the magnitude of the charge, and $B$ is the magnitude of the magnetic field.

Motion of Charged Particles in Parallel Electric and Magnetic Fields

• If the electric field and magnetic field are parallel to each other, the net force on a charged particle depends on the velocity of the particle.
• If the velocity of the charged particle is zero, the net force experienced by the particle is only due to the electric field: $\vec{F} = q\vec{E}$
• If the velocity of the charged particle is non-zero, the net force experienced by the particle is due to the electric field and the cross product of velocity and the magnetic field: $\vec{F} = q\vec{E} + q\vec{v} \times \vec{B}$
• The charged particle experiences a combination of electric and magnetic forces, resulting in a curved path.

Velocity Selector

• A velocity selector is a device that selects charged particles with a specific velocity.
• It consists of perpendicular electric and magnetic fields.
• The electric field is adjusted to match the velocity of the charged particles, ensuring that the net force acting on the particles is zero.
• Only the particles with the desired velocity pass through the velocity selector, while others are deflected or stopped.

Applications of Motion of Charges in Electric and Magnetic Fields

• Particle accelerators: Charged particles are accelerated in electric and/or magnetic fields to high velocities.
• Mass spectrometry: Charged particles are separated based on their masses using electric and magnetic fields.
• Cathode ray tubes: The motion of electrons in electric and magnetic fields is used in a cathode ray tube to produce images on screens.
• Magnetic resonance imaging (MRI): The concept of magnetic fields and motion of charged particles is utilized in medical imaging techniques.
• Particle detectors in physics experiments: Electric and magnetic fields are used to detect and measure the properties of charged particles.

Summary

• Electric and magnetic fields can exert forces on charged particles.
• The motion of charged particles in electric and magnetic fields can be determined by analyzing the net force acting on the particle.
• The relative orientation of electric and magnetic fields determines the resulting motion of the charged particles.
• Various applications, such as particle accelerators, mass spectrometry, and medical imaging, utilize the principles of motion of charges in electric and magnetic fields.
• Understanding this concept is essential for a deeper understanding of electromagnetism and its applications.

Slide 21

• Application in Cathode Ray Tubes
  • Cathode ray tubes (CRTs) use the motion of charged particles in electric and magnetic fields to produce images.
  • In a CRT, a beam of electrons is accelerated by electric fields and then deflected using magnetic fields to scan across a phosphor-coated screen, creating an image.
  • The deflection of the electrons in the CRT is based on the principles of motion of charges in electric and magnetic fields.
• Example: The operating principle of a television or computer monitor that uses a CRT.
• Equation: The force on an electron in an electric and magnetic field: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$

Slide 22

• Application in Particle Accelerators
  • Particle accelerators use powerful electric and magnetic fields to accelerate charged particles to high velocities.
  • By applying alternating electric fields, the charged particles gain energy as they pass through accelerating structures.
  • Magnetic fields are used to confine and steer the particles along a specific path.
• Example: The Large Hadron Collider (LHC) at CERN, which is used to accelerate particles such as protons and ions to high energy levels for studying fundamental particles.
• Equation: The force on a charged particle in an electric field: $\vec{F} = q\vec{E}$

Slide 23

• Application in Mass Spectrometry
  • Mass spectrometry is a technique used to analyze the masses and structures of molecules and atoms.
  • Charged particles are separated based on their mass-to-charge ratios using electric and magnetic fields.
  • The motion of charged particles in these fields allows for the identification and quantification of substances in a sample.
• Example: Mass spectrometry is used in forensic analysis, drug testing, and environmental monitoring.
• Equation: The radius of the circular path of a charged particle in a magnetic field: $r = \frac{mv}{|q|B}$

Slide 24

• Application in Magnetic Resonance Imaging (MRI)
  • MRI is a medical imaging technique that uses a combination of strong magnetic fields and radio waves to generate detailed images of the body’s internal structures.
  • The concept of magnetic fields and the motion of charged particles is utilized in MRI machines to create images with high resolution and contrast.
• Example: MRI is commonly used to diagnose and monitor various medical conditions, including brain and spinal cord disorders.
• Equation: The force on a charged particle in a magnetic field: $\vec{F} = q\vec{v} \times \vec{B}$

Slide 25

• Application in Particle Detectors in Physics Experiments
  • Electric and magnetic fields are used in particle detectors to detect and measure the properties of charged particles produced in high-energy physics experiments.
  • Charged particles passing through electric and magnetic fields can be deflected or their energy can be measured, allowing for the identification and study of different particles.
• Example: The Large Electron-Positron (LEP) Collider used electric and magnetic fields in its detectors to observe high-energy particle interactions.
• Equation: The net force on a charged particle in electric and magnetic fields: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$

Slide 26

• Key Points
  • Electric and magnetic fields can exert forces on charged particles.
  • The motion of charged particles in electric and magnetic fields is determined by the net force acting on them.
  • Different arrangements of electric and magnetic fields lead to different types of motion, such as circular or curved paths.
  • Numerous applications, including cathode ray tubes, particle accelerators, mass spectrometry, MRI, and particle detectors, utilize the principles of motion of charged particles in electric and magnetic fields.

Slide 27

• Summary
  • The motion of charges in the presence of electric and magnetic fields can be understood through various experiments, such as JJ Thomson’s experiment.
  • The interaction of charged particles with electric and magnetic fields leads to the generation of forces that affect their motion.
  • The principles of motion of charges in electric and magnetic fields find applications in various fields, including electronics, particle physics, and medical imaging.
  • Understanding these principles is essential for a comprehensive understanding of electromagnetism and its applications.

Slide 28

• Important Equations
  • Principle of superposition of electric fields: $\vec{E}_{\text{net}} = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + … + \vec{E}_n$
  • Force on a charged particle in an electric field: $\vec{F} = q\vec{E}$
  • Force on a charged particle in a magnetic field: $\vec{F} = q\vec{v} \times \vec{B}$
  • Net force on a charged particle in electric and magnetic fields: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$
  • Radius of circular path in a magnetic field: $r = \frac{mv}{|q|B}$

Slide 29

• Study Tips
  • Understand the basic concepts of electric and magnetic fields and their interactions with charged particles.
  • Practice solving numerical problems involving motion of charges in electric and magnetic fields.
  • Relate the principles to real-world applications in various fields to enhance understanding.
  • Review the experimental evidence and historical discoveries that led to the understanding of motion of charges in electric and magnetic fields.

Slide 30

• References
  • Textbooks: “Fundamentals of Physics” by Halliday, Resnick, and Walker
  • Online resources: Khan Academy, Physics Classroom, HyperPhysics
  • Research papers and scientific journals: IEEE Transactions on Magnetics, Physical Review Letters, Journal of Applied Physics