Question

Can someone please help me with this? I'll rate you if everything is correct. I'm not sure if my first part is correct, but PLEASE do all parts

You are working on a research project in which you must control the direction of travel of electrons using deflection plates. You have devised the apparatus shown in the figure below. d E V; + + + + + + The plates are of length f = 0.250 m and are separated by a distance d = 1.68 cm. Electrons are fired at v; = 5.10 x 10 m/s into a uniform electric field from the left edge of the lower, positive plate, aimed directly at the right edge of the upper, negative plate. Therefore, if there is no electric field between the plates, the electrons will follow the broken line in the figure. With an electric field existing between the plates, the electrons will follow a curved path, bending downward. (a) Determine the range of angles (in degrees) over which the electron can leave the apparatus. (Assume is measured counterclockwise from the +x-axis. Enter your answers as a comma-separated list from smallest to largest. Do not enter units in your answer.) (Omin, Omax) = -3.85, 3.85 ) (b) Determine the electric field (in N/C) required to give the maximum possible deviation angle. (Enter the magnitude.) NIC

Answer 1

Given; Length of the plate is L = 0.25m Separation distance between the plates is d=1.68 cm Electrons are fired at the speed of v; = 5.10x 10 m/s

L y d 2 Ē Vi + + + + + + + +

(a) The electric field acting on the electron inside he apparatus is F =-eĒ F = -eEų

The acceleration of the electron inside the apparatus ma = -eEy E â= m

(t) = Ū; + āt t(t) = 0; Cos 6,4 + ; sin 6 g Et -ý m e Et (t) = 0; cos 0; î + ; sin ; CE ý (1) m The x-xomponent of the velocity doesn't change with time Time taken by electron to come out from the apparatus is t = U; cos;

Equation (1) can be written as follows üſt = = 0; cos 0 t + i sin 0; eEl mu, cos y U; cos,

The angle at which electron leaves the apparatus with respect to x-axis is given by tan e El tan v; sin ; mu; cose; U; cose, Omar correspond to E = 0 tan Omar Vi sin ; U; cose tanmaz tan Вmax = 0; d tan; 7 = tan -1 (6) (6) Omar = tan

Minimum angle occurs when the electron leaves just above the right corner of the lower plate. Net displacement along the y-axis inside the apparatus to be zero y = y + + zat y = 0; sin et E -42 2m CE 2m 0=tW; sin 0 + (vis U; sin , CE -t 2m 0 putting the value of t = U; cose E 2mv sine; cose; el

Substitute E into the equation(1),we have X tan min tanmin el Vi sin , 2mo sin 0; cos; mo; cos, el U; cose; 0; sin 0; -20; sin U; cose; -U; sin , U; cose, – tan; Amin = -6 tan min tan min

0; = tan (6) =tan-1 1.68 x 10-2 0.250 0; = 3.43° Hence, the range of angle is from min = -3.84 to Omar = 3.84°

(b) The electric field require for maximum possible deviation is 2mv sin 6; cose E= el E mv sin 20; el 9.11 x 10-31 x (5.1x 106)2 x sin(2 x3.84) E 1.6 x 10-19 x 0.250 E = 79.3N/C Hence the electric field require for maximum possible deviation is 79.3N/C

(a) The range of angle is from min = -3.84º to Omar = 3.84 (b) The electric field require for maximum possible deviation is 79.3N/C

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