In Fig. 22-41, particle 1 of charge q1 = -5.00q and particle 2 of charge q2=+2.00q are fixed to an x axis. (a) As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero? (b)Sketch the net electric field lines between and around the particles.
Using the concept of the electric field at a given point, we can get the value of an individual electric field by a charge. Again using the superposition law, we can get the value of the electric field in its direction and this determines the net electric field at that point. Equating the net field to zero will give to the required coordinate.
The magnitude of the electric field, (i)
where, R = The distance of field point from the charge
q = charge of the particle
According to the superposition principle, the electric field at a point due to more than one charges, data-custom-editor="chemistry" (ii)
In the region, x<0, the fields are opposite but unequal (since E1 is everywhere bigger than E2 in this region), so there is no possibility of cancellation of the fields. In the region between the charges 0 < x < L both the fields will add up as they point in the same direction, so net field cannot be zero. In the region x > L, the fields are opposite and unequal, so the net field in this range using equation (ii) is given as:
Though , the net electric field can be zero, since these points are closer to q2 as compared to q1. Thus, we look for the zero net field point in the region x > L using equation (i) as:
Hence, the value of the x-coordinate is 2.72 L
the field lines around the particles are shown in the figure below:
Question: At some instant the velocity components of an electron moving between two charged parallel plates are and. Suppose the electric field between the plates is uniform and given byrole="math" localid="1662552218156" .In unit-vector notation, what are (a) the electron’s acceleration in that field and (b) the electron’s velocity when its x coordinate has changed by 2.0 cm?
Two charged beads are on the plastic ring in Fig. 22-44a. Bead 2, which is not shown, is fixed in place on the ring, which has radius . Bead 1, which is not fixed in place, is initially on the x-axis at angle . It is then moved to the opposite side, at angle , through the first and second quadrants of the x-y coordinate system. Figure 22-44b gives the x component of the net electric field produced at the origin by the two beads as a function of, and Fig. 22-44c gives the y component of that net electric field. The vertical axis scales are set by and . (a) At what angle u is bead 2 located? What are the charges of (b) bead 1 and (c) bead 2?
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