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Questions and Answers
What is the primary purpose of the experiment described?
What is the primary purpose of the experiment described?
Which equation relates the Lorentz force to the variables of the system?
Which equation relates the Lorentz force to the variables of the system?
What physical quantity does the equation e/m = (2V) / (B r^2) calculate?
What physical quantity does the equation e/m = (2V) / (B r^2) calculate?
Which force acts on the electron moving in a magnetic field perpendicular to its velocity?
Which force acts on the electron moving in a magnetic field perpendicular to its velocity?
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What is the maximum voltage output of the CR Tube power supply?
What is the maximum voltage output of the CR Tube power supply?
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How is the kinetic energy of the electron described in relation to potential difference?
How is the kinetic energy of the electron described in relation to potential difference?
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How long should the filament be allowed to heat up after switching on the power supply?
How long should the filament be allowed to heat up after switching on the power supply?
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In the experiment's apparatus, what gas is used in the cathode ray tube?
In the experiment's apparatus, what gas is used in the cathode ray tube?
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What current value should be set for the coils during the experiment?
What current value should be set for the coils during the experiment?
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What happens to helium atoms when electrons of high kinetic energy collide with them?
What happens to helium atoms when electrons of high kinetic energy collide with them?
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What does the characteristic green color observed in the experiment indicate?
What does the characteristic green color observed in the experiment indicate?
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What action should be taken if the beam does not fall on the 5 cm cross bar?
What action should be taken if the beam does not fall on the 5 cm cross bar?
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What is the purpose of adjusting the anode voltage in the experiment?
What is the purpose of adjusting the anode voltage in the experiment?
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What observed phenomenon indicates that the beam is being deflected in the opposite direction?
What observed phenomenon indicates that the beam is being deflected in the opposite direction?
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How should the measurements for the diameters of the circles be recorded?
How should the measurements for the diameters of the circles be recorded?
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What is the diameter of the orbit that should be recorded initially?
What is the diameter of the orbit that should be recorded initially?
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What is the shape of the path taken by a charged particle, such as an electron, in a homogenous magnetic field?
What is the shape of the path taken by a charged particle, such as an electron, in a homogenous magnetic field?
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What is the role of the European magnetic compass in the experiment?
What is the role of the European magnetic compass in the experiment?
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In the formula $B = \frac{0.716 \mu_0 N I}{R}$, what does the variable $R$ represent?
In the formula $B = \frac{0.716 \mu_0 N I}{R}$, what does the variable $R$ represent?
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Why is it beneficial to use a pair of Helmholtz Coils in the experiment?
Why is it beneficial to use a pair of Helmholtz Coils in the experiment?
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What does the permeability constant $\mu_0$ represent in the given formula?
What does the permeability constant $\mu_0$ represent in the given formula?
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Which of the following best describes the force acting on the electron in the magnetic field?
Which of the following best describes the force acting on the electron in the magnetic field?
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What is the maximum voltage that can be set using the anode voltage control in the experiment?
What is the maximum voltage that can be set using the anode voltage control in the experiment?
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How is the diameter of the electron beam measured in this experiment?
How is the diameter of the electron beam measured in this experiment?
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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
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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.
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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.
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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.
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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
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Cathode Ray Tube: A specialized tube used to directly observe the path of electrons.
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Helium Gas: The tube is filled with low-pressure helium gas.
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Electron Acceleration: Electrons emitted by a heated cathode and accelerated by a potential difference.
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Magnetic Field: A homogeneous magnetic field created by a current flowing through Helmholtz coils, deflecting electrons in the tube.
Calculation of Magnetic field
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Helmholtz Coils: The apparatus uses Helmholtz coils to achieve a uniform magnetic field at the center.
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Magnetic Field Equation: The magnetic field at the center of the Helmholtz coils is given by B = 0.716µ₀NI/R, where:
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µ₀ is the permeability constant.
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N is the number of turns in each coil.
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I is the current in the coils.
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R is the radius of the coils.
Procedure
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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.
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Voltage and Current Control: Using the black knobs on the power supply to control accelerating voltage (V) and current (I) through the Helmholtz coils.
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Beam Diameter Measurement: Measuring the diameter (2r) of the electron beam using the phosphor coated crossbars.
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Accelerating Voltage: Adjusting the accelerating voltage (V) to obtain the desired diameter of the electron beam to fall on the crossbars.
Data Analysis
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Magnetic Field Calculation: Calculating the magnetic field (B) using the equation above and measured current and radius values.
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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.
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Percent Difference: Calculating the percent difference between the experimental and accepted values of e/m.
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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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Description
Explore the principles behind measuring the charge-to-mass ratio (e/m) of an electron in electric and magnetic fields. This quiz covers the key concepts, including the Lorentz force and the relationship between kinetic energy and potential difference. Test your understanding of circular motion and the derived formula for calculating e/m.
