Two charged beads are on the plastic ring in Figure ( a ). Bead 2, which is not

Question

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 R = 61.5 cm. Bead 1 is initially on the x axis at angle = 0o. It is then moved to the opposite side, at angle = 180o, 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 (c) below gives the y component. The vertical axis scales are set by Exs = 6.15 × 104 N/C and Eys = -11.07 × 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?

Explanation / Answer

a)The bead 2 is located at 270 degree because the electric field in y-direction is due to this.

Using this fact, we know that 180 degrees the only field acting on the origin in the X direction is from Bead 1. The same applies for the y-direction in 180 and 0 degrees with Q2 being the only field acting on it.

b)The x-component of the field (6.15*10^4 N/C) at the origin when = 0° is caused entirely by bead 1. This allows us to deduce the charge on bead 1 by Coulomb's law:

F = kQq/(r^2)

Therefore, the electric field (E) at a point r distance away from a charge Q is given by:

E = F/q = kQ/(r^2)

We know the field to have a magnitude of 6.15*10^4 N/C.

Therefore, 6.15*10^4 = kQ/(0.615^2)

Q = 2.58*10^(-6) C = charge on bead 1

We know the charge to be positive as the field is directed away from the bead.


2) We might use the same reasoning to determine the charge on bead 2, as the y-component of the field when = 0° is caused entirely by bead 2 (which the symmetry of the graphs allow us to determine is fixed to the very top of the circle at the coordinates x=0m, y=0.615m).

Therefore, as we know the magnitude of the y-component of the field to be -11*10^4 N/C:

E = kQ/(r^2) = -11*10^4 N/C

kQ/(0.615^2) = -11*10^4 N/C

Q =- 4.62*10^6 C = charge on bead 2

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