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Midterm 1_270_11 Problem 4 Solution

Midterm 1_270_11 Problem 4 Solution - v = ˆ e θ v F = m a...

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Name: Problem 4 : (15) A beam of charged particles enter into a region of magnetic field B moving with the same speed V along the x-axis and complete half a revolution as shown in the figure. The beam consists of two types of particles with the same charge q but one type of particles is heavier than the other. a. Are they all positively or negatively charged? Explain. (4) At the entrance to the B region v = ˆ e x v B = ˆ e z B F = q v × B = qvB [ ˆ e x × ( ˆ e z )] = qvB ˆ e y Force in positive y- direction if q positive. At all other locations force towards the center. Both positively charged particles b. If the mass of particles with diameter D 2 is m 2 and of those with diameter D 1 is m 1 , find the mass m 2 in terms of m 1 and other given variables. Which type particles are heavier? (4) After they entered the magnetic field region
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Unformatted text preview: v = ˆ e θ v F = m a = qvB [ ˆ e × ( − ˆ e z )] = − qvB ˆ e r Central force mv 2 / r = qvB r = mv / qB Particle gyroradius proportional to m D 2 / D 1 = m 2 / m 1 m 2 = ( D 2 / D 1 ) m 1 m 2 is heavier and has a larger gyroradius D 2 D 1 x y v B c. If possible, find the magnitude (in terms of the given variables) and direction of an electric field that can make the whole beam go through the region in a straight line instead of the shown half-circles. If it is not possible, explain why not . (7) In order to move along the x-axis the magnetic force should be balanced by the electric force so that F = q [ E + v ˆ e x × ( − ˆ e z ) B ] = E = vB ( ˆ e x × ˆ e z ) = − vB ˆ e y...
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