Question

[A] To determine the electric field at the focus of a parabolic segment of charge, the simplest approach to calculate the answer is to use Colomb

Answer #1

A)

The advantages of using this method is

1) By symmetry, only one component of electric field is
non-zero

We can split a line element into sine and cosine components. If we
take two such line elements symmetrically placed in the y axis,
then the cosine components will add up and the sine components will
cancel out so the integration will be easy.

2) We can not apply Gauss's law here.

It is very difficult to construct a Gaussian surface at the point
we want to calculate the electric field.

**Example: Electric field at the center of circular arc
carrying a charge Q**

Take the radius of the arc to be R, length, L and theta is the
angle subtends with y-axis

If **N** is the linear charge density, **dq = N
dL**, dq is the element of charge occupies in the element of
length dL

Take the constant 1/(4 pi x epsilon naught) =
**k**

We can use the symmetry of the circular arc to calculate the
electric field. From the center of the circular arc, consider two
points equidistant from the center. The y components of the
electric fields adds up and the x components cancels out. Here
theta is the angle subtended to y axis.

**B)**

**Step 1: Calculate the work done in bringing each
individual charges.**

1) Work done in bringing q1 from infinity

W1 = 0 since there is no charge to attract or repel q1.

2)Work done in bringing q2 from infinity.

There is only an attractive force from q1

?W2 = k (-q1 x q2)/d

?3)Work done in bringing q3 from infinity.

?There is attraction from q2 and repelsion from q1

?Here the distance between q1 and q3 is 1.414 d.

?W3 = k(-q1x -q3) / (1.414d) + k(-q3 x q2)/d.

4) work done in bringing q4 from infinity.

There is attraction from q1, repulsion fom q2 and attraction from
q3

?q1 and q3 are are at a distance d from q4 and q2 is at a distance
of 1.414 d from q2

W4 = k(q4 x -q3) / d + k (q4 x q2) / 1.414d + k(q4 x -q1)/d.

**Step 2: Add all the work to get the potential
energy**

Here q1 = q2 = q3 = q4 = q

W = W1 + W2 + W3 + W4

? 0 + [-kq^{2}/d] + [-kq^{2}/d
+kq^{2}/1.414d] + [-kq^{2}/d +
kq^{2}/1.414d - kq^{2}/d]

= -4kq^{2}/d + 2kq^{2}/1.414d =
**- 2.58 kq ^{2}/d.**

The energy is negative in the sense there is no work done on the system, ie for assembling this configuration , no external force is required and we need exactly this much energy to de disassemble this system

Find the electric field at distance Y at point p above the
straight-line segment of Length L with linear charge density λ.
Point p is located at 1/3 L from the left of the line. Hint: in
this problem you need to find both X and Y components of the
electric field.

Find the electric field at distance Y at point
p above the straight-line segment of length L with
linear charge density λ. Point P is located at 1/3 L from the left
end of the line.
Hint: in this problem you need to find both X and Y
components of the electric field.

Calculate the electric field a distance r from a line of
electric charge infinite in extent with linear charge density
λ.

Which of the following statements is true concerning a charge in
an electric field?
- The force acting on the charge is perpendicular to the
electric field.
- The force acting on the charge is proportional to the electric
field.
- The force acting on the charge is independent of the electric
field.
- The force acting on the charge is in the same direction as the
electric field.

Give examples and describe electric charge and electric
field.

Using the symmetry of the arrangement, determine the direction
of the electric field at the center of the square at the location
of charge q in the figure below, given that qa = qb = �2.65 ?C and
qc = qd = 2.65 ?C. Calculate the magnitude of the electric field at
the location of q, given that the square is 5.65 cm on a side.

Field Sources:
Consider the following electric field (where ? and ? are
constants):
?(?, ?) = ? cos[? (? − ??)] ̂?
(a) What is the charge density ?(?, ?) associated with this
E-field? By unit analysis, what must be the units of the parameters
? and ??
(b) Given this electric field, come up with the simplest
possible magnetic field ?(?, ?) that satisfies Faraday’s law. (What
is the required magnitude of the B-field?)
(c) Show that the remaining...

An electric field E exerts a force F on an ion of charge q. At
right angles to the electric field is a magnetic field B. a. Write
an equation for the speed of the ion if the electric and magnetic
forces are equal and opposite. b. Calculate the speed if the charge
of the ion is 1.6E-19 C, the electric field is 6.0E6 N/C, and the
magnetic field is 0.83 T. c. If the charge were twice as great,...

A. Calculate the magnitude and direction of the electric field
point at Z in the diagram below
q1=2.0*10^-5C. q2=8.0*10^-6C
- <-----60cm------------> + <------30cm----->
X. Y Z
B. A small test charge of +1.0 uC experiences an electric force
of 6.0810^-6 N to the right.
1. Determine the electric field strength at that point.
2. Calculate the force that would be exerted on a charge of
-7.2*10^-4 C located at the same point, in place of the
test charge
C. A...

Type it in clear,
Give examples of electric charge and electric field, and Briefly
descibe it.
Thanks,

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