Question

A thin rod of length l and uniform charge per unit
length λ lies along the x axis as shown figure. (a) Show that the
electric field at point P, a distance y from the rod, along the
perpendicular bisector has no x component and is given by
E=(2kλsinθ0)/y. (b) Using your result to (a), show that the field
of a rod of infinite length is given by E=2kλ/y.

Answer #1

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A thin, non conducting rod with length L lies along the positive
X-Axis with one end at the origin. The rod carries a charge
distributed along its length of λ(x) = bx/L. Determine the electric
potential along the X-Axis at the point x = 2 cm if L = 1 cm and b
= 50 pC/m. Answer = (0.17 V)

A rod of length 2l lies on the x-axis from x = −l to x = +l. The
left half of the rod carries uniform negative charge density −λ
while the right half carries a uniform positive charge density +λ.
(a) What is the net charge of each half of the rod? What is the
total charge of the entire rod? (b) Determine an exact expression
for the magnitude of the electric field at an arbitrary point along
the x-axis...

Positive electric charge QQ is distributed uniformly along a
thin rod of length 2aa. The rod lies along the xx-axis between
x=−ax=−a and x=+ax=+a (Figure 1). Calculate how much work you must
do to bring a positive point charge qq from infinity to the point
x=+Lx=+L on the xx-axis, where L>aL>a.
What does your result for the potential energy U(x=+L) become in
the limit a→0? Express your answer in terms of some or all of the
variables Q, q, a,...

Positive charge Q is distributed uniformly along a rod of length
L that lies along the x-axis from x=L to x=2L. How much charge is
contained within a segment of the rod of length dx?
Integrate to find the total electric potential at the origin
(x=0) due to the rod.
Express your answer in terms of the electric constant
ϵ0epsilon_0 and variables Q,L

A thin insulating rod of length L has a charge Q spread
uniformly along it. Point P is at a distance R from the middle
point of the rod.
What is the magnitude of the electric field, E, at point
P?

6) A rod with length "l" is lied along x-axis. The
charge density of the rod is "a". Calculate the potential of the
rod for a the point p on x-axis.
7) A rod with length "l" is lied along x-axis. The
charge density of the rod is "a". Calculate the Electric field of
the rod for a point p on x-axis.

A thin rod of length L is non-uniformly charged. The charge
density is described by the expression λ=cx, where c is a constant,
λ is the charge per length, and x is the coordinate such that x=0
is one end of the rod and x=L is the other. Find the total charge
on the rod and the electric potential at a field point just
touching the rod at the x=0 end.

A very long uniform line of charge has charge per unit length
4.80 μC/m and lies along the x-axis. A second
long uniform line of charge has charge per unit length -2.32
μC/m and is parallel to the x-axis at y1
= 0.414 m .
Part A
What is the magnitude of the net electric field at point
y2 = 0.214 mon the y-axis?
Part B
What is the magnitude of the net electric field at point
y3 = 0.616...

A very long uniform line of charge has charge per unit length
3.80 µC/m and lies along the x-axis. A second long uniform
line of charge has charge -2.00 µC/m per unit length and is
parallel to the x-axis at y = 0.400 m. What is
the net electric field (magnitude and direction) at the following
points on the y-axis?
(a) y = 0.200 m
(b) y = 0.600 m

Given a thin, straight rod of length L lying on the x axis,
extending from the originx=0 to x=L. The rod carries total charge
+Q uniformly distributed over its length. We want to find the net
electric field E du to this rod at point P (b,0) on the x axis,
with b>L (that means P lies outside (“to the right of”) the rod.
Again, let’s do it step-by-step—
(a) Sketch the setup.
(b) At an arbitrary location x somewhere...

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