In 1897, JJ Thompson discovered the electron and measured the ratio of its charge to its mass using the apparatus illustrated below, as we already discussed a few times. We are now ready to really understand the full experiment. This problem analyzes Thompson's experiment. A beam of negatively charged particles with charge q and mass m is accelerated from rest by a potential difference of AV₁ (not shown in the diagram) and passes horizontally into a region in which there is a uniform vertical magnetic field of magnitude B as shown. Your goal is to set up an electric field E over the same region such that the particles pass through undeflected - Derive an expression for the required magnitude of the electric field as a function of the quantities given (q, m, B, AV) using the following steps: (a) Decide on the DIRECTION of the magnetic force, and from that, the direction of the electric force that is needed to cancel the magnetic force. Next, decide the direction of the electric field that produces this force on our test charge. Show your reasoning.
In 1897, JJ Thompson discovered the electron and measured the ratio of its charge to its mass using the apparatus illustrated below, as we already discussed a few times. We are now ready to really understand the full experiment. This problem analyzes Thompson's experiment. A beam of negatively charged particles with charge q and mass m is accelerated from rest by a potential difference of AV₁ (not shown in the diagram) and passes horizontally into a region in which there is a uniform vertical magnetic field of magnitude B as shown. Your goal is to set up an electric field E over the same region such that the particles pass through undeflected - Derive an expression for the required magnitude of the electric field as a function of the quantities given (q, m, B, AV) using the following steps: (a) Decide on the DIRECTION of the magnetic force, and from that, the direction of the electric force that is needed to cancel the magnetic force. Next, decide the direction of the electric field that produces this force on our test charge. Show your reasoning.
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Transcribed Image Text:In 1897, JJ Thompson discovered the electron and measured the ratio of its charge to its mass
using the apparatus illustrated below, as we already discussed a few times. We are now ready to
really understand the full experiment. This problem analyzes Thompson's experiment. A beam
of negatively charged particles with charge q and mass m is accelerated from rest by a potential
difference of AV₁ (not shown in the diagram) and passes horizontally into a region in which there is
a uniform vertical magnetic field of magnitude B as shown. Your goal is to set up an electric field
E over the same region such that the particles pass through undeflected
Hill
particle
Derive an expression for the required magnitude of the electric field as a function of the quantities
given (q, m, B, AV) using the following steps:
(a) Decide on the DIRECTION of the magnetic force, and from that, the direction of the electric
force that is needed to cancel the magnetic force. Next, decide the direction of the electric field
that produces this force on our test charge. Show your reasoning.
(b) Using our expressions for the electric and magnetic forces, and the fact that we want these forces
to cancel, find the relationship between the speed v, electric field E, and magnetic field B in
order for there to be zero net electromagnetic force.
(c) Find the relationship between the speed v and the potential difference AV, using conservation
of energy.
(d) Combine the two expressions above to get E in terms of q, m, B, and AVa.
(e) Find the electric field needed to keep the particles moving in a straight line if the particles are
electrons (mass 9.1 × 10-31 kg, charge -1.6 × 10-19 C), the magnetic field strength is B=0.050
T, and the accelerating voltage is AVa=120 V.
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