Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 3.4, Problem 3.55P
(a))
To determine
The charge per unit length on the side opposite to
(b))
To determine
The net charge per unit length on the side opposite to
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Consider a rod of length L carrying a charge of q distributed uniformly over its length.
Where applicable, let V(r → ∞) = 0.
Hint
q
a. What is the voltage V at point P (at distance a away from the near end of the rod) due to the
charge over the length of the rod? Express your answer in terms of given parameters (L,q,a) and
physical constants (ke, Eo). Use underscore ("_") for subscripts and spell out Greek letters.
Hint for (a)
E =
Vp =
b. Calculate the electric field at point P by differentiating V with respect to a. Let positive sign of E
indicate direction of electric field pointing away from the rod.
Hint for (b)
a
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An infinitely large horizontal plane carries a uniform surface charge density n = -0.280 nC/m². What is the electric field
✓? A proton is traveling in this field with initial speed
strength in the region above the plane [Select]
V01.00 x 105 m/s at 0 = 30° angle with respect to the plane, as shown in the figure below. Use the coordinate system in
✓? If the zero potential is
the figure and neglect the effect of gravity. How high can the proton go
[Select]
at the origin level, i.e., y = 0 level, what is the potential energy
[Select]
height y21.00 m [Select]
y
[Select]
0
of the proton when it is at a height of y₁ = 0.500 m ? What is the proton's kinetic energy at
Vo
V
0
and kinetic energy
X
O
[HW3.1] A solid metal ball (radius a) is grounded inside a floating (isolated) metal sphere
(inner radius b, outer radius d). The sphere comes with total charge Q. Find surface charge
density on every surface (the outer surface of the metal ball, inner and outer surface of the
sphere), and capacitance of the system.
Chapter 3 Solutions
Introduction to Electrodynamics
Ch. 3.1 - Find the average potential over a spherical...Ch. 3.1 - Prob. 3.2PCh. 3.1 - Prob. 3.3PCh. 3.1 - Prob. 3.4PCh. 3.1 - Prob. 3.5PCh. 3.1 - Prob. 3.6PCh. 3.2 - Find the force on the charge +q in Fig. 3.14....Ch. 3.2 - (a) Using the law of cosines, show that Eq. 3.17...Ch. 3.2 - In Ex. 3.2 we assumed that the conducting sphere...Ch. 3.2 - A uniform line charge is placed on an infinite...
Ch. 3.2 - Two semi-infinite grounded conducting planes meet...Ch. 3.2 - Prob. 3.12PCh. 3.3 - Find the potential in the infinite slot of Ex. 3.3...Ch. 3.3 - Prob. 3.14PCh. 3.3 - A rectangular pipe, running parallel to the z-axis...Ch. 3.3 - A cubical box (sides of length a) consists of five...Ch. 3.3 - Prob. 3.17PCh. 3.3 - Prob. 3.18PCh. 3.3 - Prob. 3.19PCh. 3.3 - Suppose the potential V0() at the surface of a...Ch. 3.3 - Prob. 3.21PCh. 3.3 - In Prob. 2.25, you found the potential on the axis...Ch. 3.3 - Prob. 3.23PCh. 3.3 - Prob. 3.24PCh. 3.3 - Find the potential outside an infinitely long...Ch. 3.3 - Prob. 3.26PCh. 3.4 - A sphere of radius R, centered at the origin,...Ch. 3.4 - Prob. 3.28PCh. 3.4 - Four particles (one of charge q, one of charge 3q,...Ch. 3.4 - In Ex. 3.9, we derived the exact potential for a...Ch. 3.4 - Prob. 3.31PCh. 3.4 - Two point charges, 3qand q , arc separated by a...Ch. 3.4 - Prob. 3.33PCh. 3.4 - Three point charges are located as shown in Fig....Ch. 3.4 - A solid sphere, radius R, is centered at the...Ch. 3.4 - Prob. 3.36PCh. 3.4 - Prob. 3.37PCh. 3.4 - Here’s an alternative derivation of Eq. 3.10 (the...Ch. 3.4 - Prob. 3.39PCh. 3.4 - Two long straight wires, carrying opposite uniform...Ch. 3.4 - Prob. 3.41PCh. 3.4 - You can use the superposition principle to combine...Ch. 3.4 - A conducting sphere of radius a, at potential V0 ,...Ch. 3.4 - Prob. 3.44PCh. 3.4 - Prob. 3.45PCh. 3.4 - A thin insulating rod, running from z=a to z=+a ,...Ch. 3.4 - Prob. 3.47PCh. 3.4 - Prob. 3.48PCh. 3.4 - Prob. 3.49PCh. 3.4 - Prob. 3.50PCh. 3.4 - Prob. 3.51PCh. 3.4 - Prob. 3.52PCh. 3.4 - Prob. 3.53PCh. 3.4 - Prob. 3.54PCh. 3.4 - Prob. 3.55PCh. 3.4 - Prob. 3.56PCh. 3.4 - Prob. 3.57PCh. 3.4 - Find the charge density () on the surface of a...
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- Problem 3.15 Determine the energy of the field generated by the charge Q uniformly distributed over the surface of a sphere of radius R located in free space. E2 R E1 Figure 3.26: A dielectric sphere half-submerged into a liquid dielectric.arrow_forwardProblem 2.20 One of these is an impossible electrostatic field. Which one? (a) Ek[xy x + 2yzý + 3xz2]; (b) E= k[y² + (2xy + z²) ŷ + 2yz 2]. Here k is a constant with the appropriate units. For the possible one, find the potential, using the origin as your reference point. Check your answer by computing VV. [Hint: You must select a specific path to integrate along. It doesn't matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a particular path in mind.] Problem 2.11 Use Gauss's law to find the electric field inside and outside a spherical shell of radius R, which carries a uniform surface charge density o. Compare your answer to Prob. 2.7. Problem 2.21 Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V (r).arrow_forwardConsider an infinitely long wire of charge carrying a positive charge density of A. The electric field due to λ this line of charge is given by E= 2kef= -, where is a unit vector directed radially outward Σπερμ from the infinitely long wire of charge. Hint #3 a. Letting the voltage be zero at some reference distance (V(ro) = 0), calculate the voltage due to this infinite line of charge at some distance r from the line of charge. Give your answer in terms of given quantities (A,ro,r) and physical constants (ke or Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for V(r) calculation 3 V(r) = b. There is a reason we are not setting V(r → ∞o) = 0 as we normally do (in fact, in general, whenever you have an infinite charge distribution, this "universal reference" does not work; you need a localized charge distribution for this reference to work). Which of the following best describes what happens to potential as roo? (That is, what is V(ro), with our current…arrow_forward
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