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106-20103-MT1

# 106-20103-MT1 - PROBLEM(1(25 points A rod of length L...

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Phys 106 First Midterm Examination Page 1 Saturday, 16-July, 2011 PROBLEM (1) (25 points) A rod of length L carries uniformly distributed positive total charge Q and it lies along the x axis, as shown in the figure. A charged particle with positive charge Q is located at the point x = 0, y = r . Express your answers in terms of L , Q , r , k e and unit vectors . (a) (10 pts) Find the electric field ! E 1 due to the rod at a point P that is located along the axis of the rod and a distance r from one end. Q L r P r x y Divide the rod into small segments of charge dq . P x x dx dq dE E 1 = dE = k e " " dq x 2 = k e # dx x 2 where # = Q L r r + L " E 1 = k e Q L dx x 2 r r + L " = k e Q L # 1 x \$ % & ' ( ) r r + L E 1 = k e Q L 1 r " 1 r + L # \$ % & ' ( = k e Q r ( r + L ) ! E 1 = k e Q r ( r + L ) ( " " i ) (b) (5 pts) Find the electric field ! E 2 at the point P due to the charged particle. E 2 = k e Q r 2 ! E 2 = k e Q r 2 ( " " j ) (c) (5 pts) Find the resultant field ! E at the point P . ! E = ! E 1 + ! E 2 = k e Q r ( r + L ) ( " " i ) + k e Q r 2 ( " " j ) ! E = k e Q 1 r ( r + L ) ( " " i ) + 1 r 2 ( " " j ) # \$ % & ' ( (d) (5 pts) An electron with mass m and charge – e is located at P and released from rest. Ignore any gravitational effects and find the electron's acceleration a just after it is released. Express your answer in terms of the given quantities and constants, including m and e , as needed.

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106-20103-MT1 - PROBLEM(1(25 points A rod of length L...

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