In 1897, JJ Thompson discovered the electron and measured the ratio of its charge to its massusing the apparatus illustrated below, as we already discussed a few times. We are now ready toreally understand the full experiment. This problem analyzes Thompson's experiment. A beamof negatively charged particles with charge q and mass m is accelerated from rest by a potentialdifference of AV₁ (not shown in the diagram) and passes horizontally into a region in which there isa uniform vertical magnetic field of magnitude B as shown. Your goal is to set up an electric fieldE over the same region such that the particles pass through undeflectedparticle-Derive an expression for the required magnitude of the electric field as a function of the quantitiesgiven (q, m, B, AVa) using the following steps:(a) Decide on the DIRECTION of the magnetic force, and from that, the direction of the electricforce that is needed to cancel the magnetic force. Next, decide the direction of the electric fieldthat 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 forcesto cancel, find the relationship between the speed v, electric field E, and magnetic field B inorder for there to be zero net electromagnetic force.(c) Find the relationship between the speed v and the potential difference AV₁ using conservationof energy.(d) Combine the two expressions above to get E in terms of q, m, B, and AV₁.(e) Find the electric field needed to keep the particles moving in a straight line if the particles areelectrons (mass 9.1 × 10-³1 kg, charge -1.6 × 10-19 C), the magnetic field strength is B=0.050T, and the accelerating voltage is AVa=120 V.

Given, A Thompson experiment A beam of negatively charged particles with charge q and mass m is…

Answered: using the apparatus illustrated below,…

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