Chapter 22, Problem 017 Your answer is partially correct. Try again. Two charged

Question

Chapter 22, Problem 017 Your answer is partially correct. Try again. Two charged beads are on the plastic ring in Figure (a). Bead 2, which is not shown, is fixed in place on the ring, which has radius R62.4 cm. Bead 1 is initially on the x axis at angle ? 0°. It is then moved to the opposite side, at angle ?-180°, through the first and second quadrants of the xy coordinate system. Figure (b) gives the x component of the net electric field produced at the origin by the two beads as a function of ? and Figure belo gves they component. The vertical axis scales are set y , 15 LO. and Eys =-9.27 x 104 N/C (a) At what positive angle ? is bead 2 located? (Note: bead 2 is negative charged). What are the charges of (b) bead 1 and (c) bead 2? Ring Bead 1 90° 180° 0 180°

Explanation / Answer

given there are two charged beads

bead 1 is initially at theta = 0 deg, and is moved to 180 deg through 1st and 2nd quadrants

let bead 2 be at angle phi wrt the +x axis

now, from plot b

the x component of electric field is given

when theta = 0 deg, Ex = -Exs = -5.15*10^4 N/C

when theta = 180 deg, Ex = Exs = 5.15*10^4 N/C

for y component

when theta = 0 deg, Ey = 0

when theta = 180 deg, Ey = 0

when theta = 90 deg, Ey = -Eys = -9.27*10^4 N/C

hence

Ex is 0 when bead 1 is on y axis, hence bead 2 is on y axis too

hence

a. phi = 270 deg

b. let charge on bead 1 = q1

charge on bead 2 = q2

Ey = 0 for theta = 0

hence

q2 = 0

also,

Ex = -Exs for theta = 0 deg

hence

5.15*10^4 = k*q1/0.624^2

q1 = 2.233*10^-6 C = 2.23 uC

hence

q1 = 2.23 uC

q2 = 0 C

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