E3B.9 Consider the situation described in problem E3B.8. Repeat all of the parts of that problem for the path from B to C instead of A to B. (That is, in the statement of that problem, replace "A" by "B" and "B" by "C" everywhere.)

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Chapter1: Units, Trigonometry. And Vectors
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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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The question  is E3B.9

E3B.9
Part(a)
The components of dr can be taken fror
As from B to C, the only component is
So,
dr = dy ĵ
part(b)
Since electric Field E is constant, we l
E
.
É dĩ = (-4001+ 300i). (dy i)
E = (-400î + 300ĵ)]
as
From, above expression,
it is clear that E dr has the same valu
Part(e)
Now,
E dr can be calculated as,
²³ E · d² = E(Tв - 7c)
⇒E - (TB-7A) = (-4001+300). [(1
= 300 dy
as, Tв = (11î + 6ĵ) and 7c = (11î +î)
So,
Ẻ · († B − TA) = (-400î + 300ĵ) · (6î) ·
E
=
So
/ E. dr = 1800 V
Transcribed Image Text:E3B.9 Part(a) The components of dr can be taken fror As from B to C, the only component is So, dr = dy ĵ part(b) Since electric Field E is constant, we l E . É dĩ = (-4001+ 300i). (dy i) E = (-400î + 300ĵ)] as From, above expression, it is clear that E dr has the same valu Part(e) Now, E dr can be calculated as, ²³ E · d² = E(Tв - 7c) ⇒E - (TB-7A) = (-4001+300). [(1 = 300 dy as, Tв = (11î + 6ĵ) and 7c = (11î +î) So, Ẻ · († B − TA) = (-400î + 300ĵ) · (6î) · E = So / E. dr = 1800 V
E3B.8 Consider a region of space where the electric field is
everywhere equal to É = [-400, +300, 0] N/C.
A
-10 cm
E
B
C
A
We'd like to calculate the potential difference - A
between points A and B. We will do this by dividing the
straight-line path going from A to B into 20 equal steps,
which we will consider to be "sufficiently small" steps.
(a) List the components of dr for each step.
(b) Argue that Ē. dr has the same value for each step and
compute that value. (Hint: Use the component expres-
sion for the dot product.)
(c) Calculate the value of E. dr in this case.
(d) Calculate the potential difference B - ₁. If the poten-
tial at A is -5 V, what is the potential at B?
(e) In this particular case, show that SË • dr = Ë• A7,
where Ar is the entire displacement from A to B? What
would have to be different about the electric field to
makeJE•dĩ#Ẻ•A
E3B.9
Consider the situation described in problem E3B.8.
Repeat all of the parts of that problem for the path from
B to C instead of A to B. (That is, in the statement of that
problem, replace "A" by "B" and "B" by "C" everywhere.)
Transcribed Image Text:E3B.8 Consider a region of space where the electric field is everywhere equal to É = [-400, +300, 0] N/C. A -10 cm E B C A We'd like to calculate the potential difference - A between points A and B. We will do this by dividing the straight-line path going from A to B into 20 equal steps, which we will consider to be "sufficiently small" steps. (a) List the components of dr for each step. (b) Argue that Ē. dr has the same value for each step and compute that value. (Hint: Use the component expres- sion for the dot product.) (c) Calculate the value of E. dr in this case. (d) Calculate the potential difference B - ₁. If the poten- tial at A is -5 V, what is the potential at B? (e) In this particular case, show that SË • dr = Ë• A7, where Ar is the entire displacement from A to B? What would have to be different about the electric field to makeJE•dĩ#Ẻ•A E3B.9 Consider the situation described in problem E3B.8. Repeat all of the parts of that problem for the path from B to C instead of A to B. (That is, in the statement of that problem, replace "A" by "B" and "B" by "C" everywhere.)
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