Measurement of e/m of the Electron

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Questions and Answers

What is the primary purpose of the experiment described?

  • To measure the mass of an electron
  • To study the interaction of charged particles with light
  • To calculate the speed of electrons in a vacuum
  • To study the effect of electric and magnetic fields on charged particles (correct)

Which equation relates the Lorentz force to the variables of the system?

  • F = e v B (correct)
  • F = eV / m
  • F = m v^2 / r
  • F = m g

What physical quantity does the equation e/m = (2V) / (B r^2) calculate?

  • Mass of the electron
  • Charge to mass ratio of the electron (correct)
  • Kinetic energy of the electron
  • Charge of the electron

Which force acts on the electron moving in a magnetic field perpendicular to its velocity?

<p>Lorentz force (A)</p> Signup and view all the answers

What is the maximum voltage output of the CR Tube power supply?

<p>500 V (A)</p> Signup and view all the answers

How is the kinetic energy of the electron described in relation to potential difference?

<p>It is directly proportional to the potential difference (D)</p> Signup and view all the answers

How long should the filament be allowed to heat up after switching on the power supply?

<p>1-2 minutes (D)</p> Signup and view all the answers

In the experiment's apparatus, what gas is used in the cathode ray tube?

<p>Helium (B)</p> Signup and view all the answers

What current value should be set for the coils during the experiment?

<p>1.8 A (C)</p> Signup and view all the answers

What happens to helium atoms when electrons of high kinetic energy collide with them?

<p>They ionize partially (D)</p> Signup and view all the answers

What does the characteristic green color observed in the experiment indicate?

<p>The presence of ionized helium atoms (A)</p> Signup and view all the answers

What action should be taken if the beam does not fall on the 5 cm cross bar?

<p>Increase the coil current and decrease the anode voltage (A)</p> Signup and view all the answers

What is the purpose of adjusting the anode voltage in the experiment?

<p>To control the beam's path diameter (D)</p> Signup and view all the answers

What observed phenomenon indicates that the beam is being deflected in the opposite direction?

<p>Reversing the current leads (C)</p> Signup and view all the answers

How should the measurements for the diameters of the circles be recorded?

<p>In Table 1 under their respective diameters (A)</p> Signup and view all the answers

What is the diameter of the orbit that should be recorded initially?

<p>5 cm (C)</p> Signup and view all the answers

What is the shape of the path taken by a charged particle, such as an electron, in a homogenous magnetic field?

<p>A circle (C)</p> Signup and view all the answers

What is the role of the European magnetic compass in the experiment?

<p>To determine the North-South direction (B)</p> Signup and view all the answers

In the formula $B = \frac{0.716 \mu_0 N I}{R}$, what does the variable $R$ represent?

<p>The radius of the coils (B)</p> Signup and view all the answers

Why is it beneficial to use a pair of Helmholtz Coils in the experiment?

<p>They provide a uniform magnetic field near the center (A)</p> Signup and view all the answers

What does the permeability constant $\mu_0$ represent in the given formula?

<p>Magnetic permeability of free space (A)</p> Signup and view all the answers

Which of the following best describes the force acting on the electron in the magnetic field?

<p>It is always at right angles to the velocity of the electron (C)</p> Signup and view all the answers

What is the maximum voltage that can be set using the anode voltage control in the experiment?

<p>500 volts (C)</p> Signup and view all the answers

How is the diameter of the electron beam measured in this experiment?

<p>By allowing the beam to fall on phosphor coated cross bars (C)</p> Signup and view all the answers

Flashcards

Electron's charge-to-mass ratio (e/m)

A fundamental constant that represents the ratio of an electron's charge to its mass, measured in Coulombs per kilogram.

Lorentz force

The force exerted on a charged particle moving within a magnetic field.

Circular motion of electron

The path an electron follows when subjected to a perpendicular magnetic field.

Kinetic energy

Energy of motion possessed by charged particles.

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Accelerating voltage

Voltage used to accelerate charged particles, like electrons.

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Magnetic field

Region of space where a magnetic force is detectable

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Radius of circular path

The distance from the center of the circular path to the electron path in a magnetic field

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Cathode Ray Tube (CRT)

A vacuum tube used to study electron beam behavior.

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Helmholtz Coils

A pair of circular coils used to produce a uniform magnetic field. Specifically placed to achieve uniform field at center.

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Magnetic Field (B)

A region around a magnet or electric current where a magnetic force can be detected.

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Cathode Ray Tube

A vacuum tube that uses an electron beam to create a visual display.

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Magnetic Force (F)

The force exerted on a charged particle moving in a magnetic field.

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Accelerating Voltage (V)

Voltage applied to accelerate charged particles, like electrons, in a vacuum tube.

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Permeability Constant (µ₀)

A constant describing the ability of a material to permit the passage of magnetic flux.

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Importance of aligning coils with Earth's field.

To avoid the interference of the Earth's magnetic field with the experiment, that can significantly affect the experiment results, creating a greater variability or noise.

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Measuring Electron Beam Diameter (2r)

Determining the width of the electron beam by measuring the distance across the beam as it hits the phosphor screen.

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Filament current

The electric current flowing through the filament in the electron gun, heating it up to emit electrons.

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Anode voltage

The voltage difference between the anode and cathode, accelerating electrons towards the anode.

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Electron beam

A stream of electrons emitted from the electron gun and accelerated by the anode voltage.

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Beam deflection

The change in the electron beam's direction when it passes through a magnetic field.

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Electron path in a magnetic field

The circular or helical path followed by an electron when moving through a magnetic field.

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Radius of the electron path

The distance from the center of the electron's circular path to the electron's location.

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What happens when the coil current is reversed?

The direction of the magnetic field, produced by the coils, is reversed, causing the electron beam to deflect in the opposite direction.

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Study Notes

Measurement of e/m of the Electron

  • Purpose: To study the effect of electric and magnetic fields on charged particles. To measure the charge-to-mass ratio (e/m) of an electron.

Theory

  • Lorentz Force: When an electron moves in a magnetic field (B) perpendicular to its velocity (v), it experiences a force (F) perpendicular to both B and v, calculated as F = evB.

  • Circular Motion: This force causes the electron to move in a circular path in a plane perpendicular to the magnetic field. Applying Newton's second law (F=ma) for circular motion, this leads to evB= mv²/r.

  • Kinetic Energy: If the electron was accelerated from rest by a potential difference (V), its kinetic energy (½mv²) equals the loss in potential energy (eV), where m is the mass and e is the magnitude of the charge.

  • e/m Calculation: Combining the equations for the Lorentz force in circular motion and kinetic energy yields the formula e/m = 2V/B²r². This means we can calculate e/m using known values for voltage (V), magnetic field (B), and radius of the circular path (r).

Apparatus

  • Cathode Ray Tube: A specialized tube used to directly observe the path of electrons.

  • Helium Gas: The tube is filled with low-pressure helium gas.

  • Electron Acceleration: Electrons emitted by a heated cathode and accelerated by a potential difference.

  • Magnetic Field: A homogeneous magnetic field created by a current flowing through Helmholtz coils, deflecting electrons in the tube.

Calculation of Magnetic field

  • Helmholtz Coils: The apparatus uses Helmholtz coils to achieve a uniform magnetic field at the center.

  • Magnetic Field Equation: The magnetic field at the center of the Helmholtz coils is given by B = 0.716µ₀NI/R, where:

  • µ₀ is the permeability constant.

  • N is the number of turns in each coil.

  • I is the current in the coils.

  • R is the radius of the coils.

Procedure

  • Compass Orientation: Setting the apparatus so that the plane of the Helmholtz coils is aligned with the Earth's magnetic field. This is crucial for accurate measurements.

  • Voltage and Current Control: Using the black knobs on the power supply to control accelerating voltage (V) and current (I) through the Helmholtz coils.

  • Beam Diameter Measurement: Measuring the diameter (2r) of the electron beam using the phosphor coated crossbars.

  • Accelerating Voltage: Adjusting the accelerating voltage (V) to obtain the desired diameter of the electron beam to fall on the crossbars.

Data Analysis

  • Magnetic Field Calculation: Calculating the magnetic field (B) using the equation above and measured current and radius values.

  • e/m Calculation: Calculating the charge-to-mass ratio (e/m) by applying the equation e/m = 2V/B²r². This is done for several values of voltage and diameter to determine an average value.

  • Percent Difference: Calculating the percent difference between the experimental and accepted values of e/m.

  • Sources of Error: Listing the possible sources of error in the experiment (e.g., inaccuracies in measurements, uncertainties in apparatus alignment).

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