Problem 2: Figure 2 shows a thin rod of length L with total charge Q (distributed uniformly along the rod). Find an expression for the electric field E at point P. Give your answer in component form. a) Figure 2 shows a representative infinitesimal element dy along the rod and the field dĒ created by this element in point P. If the rod is charged uniformly along its length, what is the amount of charge dq contained in the element dy? Use it to compute the magnitude of the electric field dĒ in point P (make sure to express it in terms of x, y, and constant parameters of the system). ул y Edy > X x de FIG. 2: The scheme for Problem 2 b) Find x and y-components of the field dĒ (dEx and dEy). You can use angle 0 at the intermediate steps, but eventually express everything in terms of x, y, and constant parameters of the system. Note that one of the components must be negative (which one?). c) Integrate the x-component of de over the rod to find the x-component of the total field, Ex = f dEx (insert the limits of integration yourself). The integral that you need to use here is ſt² t₂ dt (a²+1²) 3/2 |t₂ = where t is the variable of integration, and a is a constant. You need to figure out which of a² √a²+t²t₁ the variables in dEx plays the role of the variable of integration, and what plays the role of constant a.
Problem 2: Figure 2 shows a thin rod of length L with total charge Q (distributed uniformly along the rod). Find an expression for the electric field E at point P. Give your answer in component form. a) Figure 2 shows a representative infinitesimal element dy along the rod and the field dĒ created by this element in point P. If the rod is charged uniformly along its length, what is the amount of charge dq contained in the element dy? Use it to compute the magnitude of the electric field dĒ in point P (make sure to express it in terms of x, y, and constant parameters of the system). ул y Edy > X x de FIG. 2: The scheme for Problem 2 b) Find x and y-components of the field dĒ (dEx and dEy). You can use angle 0 at the intermediate steps, but eventually express everything in terms of x, y, and constant parameters of the system. Note that one of the components must be negative (which one?). c) Integrate the x-component of de over the rod to find the x-component of the total field, Ex = f dEx (insert the limits of integration yourself). The integral that you need to use here is ſt² t₂ dt (a²+1²) 3/2 |t₂ = where t is the variable of integration, and a is a constant. You need to figure out which of a² √a²+t²t₁ the variables in dEx plays the role of the variable of integration, and what plays the role of constant a.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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I need help with question A,B, and C because my professor won't help me and I don't know how to to do the problem.
Transcribed Image Text:Problem 2: Figure 2 shows a thin rod of length L with total charge Q
(distributed uniformly along the rod). Find an expression for the electric
field E at point P. Give your answer in component form.
a) Figure 2 shows a representative infinitesimal element dy along
the rod and the field dĒ created by this element in point P. If the rod
is charged uniformly along its length, what is the amount of charge dq
contained in the element dy? Use it to compute the magnitude of the
electric field dĒ in point P (make sure to express it in terms of x, y, and
constant parameters of the system).
ул
y
Edy
>
X
x
de
FIG. 2: The scheme for Problem 2
b) Find x and y-components of the field dĒ (dEx and dEy). You can use angle 0 at the intermediate
steps, but eventually express everything in terms of x, y, and constant parameters of the system. Note
that one of the components must be negative (which one?).
c) Integrate the x-component of de over the rod to find the x-component of the total field, Ex = f dEx
(insert the limits of integration yourself). The integral that you need to use here is ſt²
t₂
dt
(a²+1²) 3/2
|t₂
=
where t is the variable of integration, and a is a constant. You need to figure out which of
a² √a²+t²t₁
the variables in dEx plays the role of the variable of integration, and what plays the role of constant a.
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