Question

Two charges are on the z-axis, charge +q at z = +a and −q at z = −a. (Hint: This is NOT a continuous charge distribution but two discrete point charges.)

(a) Find the electric potential V (x, y, z) at a field point r = (x, y, z).

(b) Find the potential V (x, y, 0) at a point (x, y, 0) on the xy-plane.

(c) What is the total electrostatic energy of this system?

(d) Using the result of part (c), find out how much work it takes to move the charges closer so that their separation is a rather than 2a.

Answer #1

Two point charges are on the y axis. A 3.10-µC charge
is located at y = 1.25 cm, and a -2-µC charge is located
at y = −1.80 cm.
(a) Find the total electric potential at the origin.
________ V
(b) Find the total electric potential at the point whose
coordinates are (1.50 cm, 0).
________ V

A line charge sits on the z-axis from z=0 to z=a. The charge
density, lambda, varies linearly with the expression:
lambda=(lambda0/a)z.
a, What is the electric potential, V, due to this line charge,
everywhere on the x-axis?
b, How much mechanical work is needed to move a charge Q from
z=+infinite to the position on the x-axis at x=d?

Two positive point
charges are held fixed on the x-axis. Point charge
A is located at the origin, and point charge
B is located at the position x = −5.00 cm =
−5.00✕10-2 m (on the negative x-axis). The
magnitude of charge A is two times greater than
that of charge B: qA =
2qB.
ke = 8.9876✕109
Nm2/C2
(A.) The electric
force on charge A has magnitude 0.344 mN =
0.344⨯10-3 N. What is the electric force (magnitude
and...

Two point charges are placed on the x-axis. The charge
+2q is at x = 1.5 m, and the charge −q
is at x = −1.5 m.
(a) There is a point on the x-axis between the two
charges where the electric potential is zero. Where is this
point?
x = ______________ m
(b) The electric potential also vanishes in one of the following
regions. Identify the appropriate region.
Is it:
Region 1: 5.0 m > x > 1.5 m...

Two charges are located on the X axis: a +300 pC charge at x =
2.0 cm, and a -400 pC charge at x = -2.0 cm. Find the X Y
components of the electric field at a point on the Y axis with the
coordinates (0, 1.0 cm).

Find the electrostatic potential of an octupole made of the
following charges: q1 = -q, q2 = +2 q, q3 = -2 q and q4 = +q, the
charges are placed along the x-axis with the following coordinates:
x1 = -2 a, x2 = -a, x3 = a and x4 = 2 a. Evaluate the potential as
an expansion in Legendre polynomials at a point P in the
xy-plane.

Two point charges are fixed on the y axis, a negative point
charge q1 = -25uC at y1 = +0.22m and a postive charge q2 at y2 =
+0.34m. A third point charge q=+8.4uC is fixed at the origin. The
net electrostatic force exerted on the charge q by the other two
charges has a magnitude of 27N and points in the +y direction.
Determine the magnitude of q2.

Consider an infinitely long flat sheet of charges of width
2a. It is parallel to the axis y and lies in
(xy) plane in between x=-a and x=+a. The
charges are distributed uniformly, with surface density σ. Find an
expression for the electrostatic field E
at height Z above the midline of the charged sheet (i.e.
above y axis).
Hint: As a starting point, you can use
the formula for infinitely long line of charges.

Two charges are fixed in place on the x-axis as shown. The
charge at x = 0 is negative and has
magnitude q = 2 μCoulombs (1 μCoulomb = 10-6
Coulombs). The charge at x = d, (d = +12
cm), is positive and has magnitude Q = 4
μCoulombs. Find a point x = xo along
the x-axis at which the electric field is zero.
xo =____cm

Two point charges of −Q and Q are fixed at x=−a and x=a on the x
axis, respectively as shown in Figure 1. Another point charge of q
and mass m is released at x=x0 at rest and it is free to move. Find
a) the electric field vector, −→E (both magnitude and direction) at
any x and b) the ultimate speed of particle of mass m.

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