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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