potential is zero QUICK QUIZ 24.4 In a certain region of space, the electric everywhere along the x axis. (i) From this information, you can conclude that the x component of the electric field in this region is (a) zero, (b) in the positive x direction, or (c) in the negative x direction. (ii) Suppose the electric potential is +2 V everywhere along the x axis. From the same choices, what can you con- clude about the x component of the electric field now?

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Quick quiz 24.4
Shot with my Chit's A22
Samsung Camera
g the electric field ►
from the potential
E
Figure 24.11 Equipotential surfaces (the dashed blue lines are intersections of these surfaces with
the page) and electric field lines. In all cases, the equipotential surfaces are perpendicular to the elec
tric field lines at every point.
charge is E = kq/r, a familiar result. Notice that the potential changes only in
the radial direction, not in any direction perpendicular to r. Therefore, V (like
E) is a function only of r, which is again consistent with the idea that equipo-
tential surfaces are perpendicular to field lines. In this case, the equipotential
surfaces are a family of spheres concentric with the spherically symmetric charge
distribution (Fig. 24.11b). The equipotential surfaces for an electric dipole are
sketched in Figure 24.11c.
In general, the electric potential is a function of all three spatial coordinates. If
V(r) is given in terms of the Cartesian coordinates, the electric field components E
E, and E can readily be found from V(x, y, z) as the partial derivatives²
Ex
av
əx
E =
av
dy
E₂
av
əz
(24.18)
QUICK QUIZ 24.4 In a certain region of space, the electric potential is zero
everywhere along the x axis. (i) From this information, you can conclude that
the x component of the electric field in this region is (a) zero, (b) in the positive
x direction, or (c) in the negative x direction. (ii) Suppose the electric potential
is +2 V everywhere along the x axis. From the same choices, what can you con-
•clude about the x component of the electric field now?
The sem
field is aim
ence A
Transcribed Image Text:Shot with my Chit's A22 Samsung Camera g the electric field ► from the potential E Figure 24.11 Equipotential surfaces (the dashed blue lines are intersections of these surfaces with the page) and electric field lines. In all cases, the equipotential surfaces are perpendicular to the elec tric field lines at every point. charge is E = kq/r, a familiar result. Notice that the potential changes only in the radial direction, not in any direction perpendicular to r. Therefore, V (like E) is a function only of r, which is again consistent with the idea that equipo- tential surfaces are perpendicular to field lines. In this case, the equipotential surfaces are a family of spheres concentric with the spherically symmetric charge distribution (Fig. 24.11b). The equipotential surfaces for an electric dipole are sketched in Figure 24.11c. In general, the electric potential is a function of all three spatial coordinates. If V(r) is given in terms of the Cartesian coordinates, the electric field components E E, and E can readily be found from V(x, y, z) as the partial derivatives² Ex av əx E = av dy E₂ av əz (24.18) QUICK QUIZ 24.4 In a certain region of space, the electric potential is zero everywhere along the x axis. (i) From this information, you can conclude that the x component of the electric field in this region is (a) zero, (b) in the positive x direction, or (c) in the negative x direction. (ii) Suppose the electric potential is +2 V everywhere along the x axis. From the same choices, what can you con- •clude about the x component of the electric field now? The sem field is aim ence A
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