A positively charged rod of length L, and uniform line charge density A, is placed along the y-axis as shown in the drawing. The origin of the coordinate system is located at the center of the rod. Calculate the electric potential (voltage) at point P on the x axis. (Express your answer in terms of L, λ, and x.)

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Am I doing part A correctly? and can you help me explain part B!
a. A positively charged rod of length L, and uniform line charge density A, is placed along the
y-axis as shown in the drawing. The origin of the coordinate system is located at the center
of the rod. Calculate the electric potential (voltage) at point P on the x axis.
{Express your answer in terms of L, A, and x.)
b. Now a point charge, q, is brought in from very, very far away, and then placed at point P,
while the charged rod remains fixed in position.
What is the change in electric potential energy of the system?
{Express your answer in terms of L, λ, q, and x.)
O EXCEPTIONS,
y axis
→→→x axis
**
X
Transcribed Image Text:a. A positively charged rod of length L, and uniform line charge density A, is placed along the y-axis as shown in the drawing. The origin of the coordinate system is located at the center of the rod. Calculate the electric potential (voltage) at point P on the x axis. {Express your answer in terms of L, A, and x.) b. Now a point charge, q, is brought in from very, very far away, and then placed at point P, while the charged rod remains fixed in position. What is the change in electric potential energy of the system? {Express your answer in terms of L, λ, q, and x.) O EXCEPTIONS, y axis →→→x axis ** X
a) dQ = Ady
Vp= Suda
kdQ
r
dEp
K Ady = (FK Idy
√x²+y²
Yi √√ x² + y²
= + ½/2/2
(KX) In (y + √ √²+y²) | ₁ = = 2 2
=
-1/₂ √x² + y²
= (K²) [In( ½ + ({√(4)³+x²) − \n(− ½ + (√(-3)*+x²))]
=
(K2) In[/=/= +
1/2 + √√( ²2 ) ² + y ²
- 2²/2/2 + √√√( ²2 ) ² + y ²
]
3
y axis
↑(0,4/2)
>
_r=√x² + y²
Di D
***
4/2
кадаг ду
dy
C
0
dep
→→→x axis
نیا
Transcribed Image Text:a) dQ = Ady Vp= Suda kdQ r dEp K Ady = (FK Idy √x²+y² Yi √√ x² + y² = + ½/2/2 (KX) In (y + √ √²+y²) | ₁ = = 2 2 = -1/₂ √x² + y² = (K²) [In( ½ + ({√(4)³+x²) − \n(− ½ + (√(-3)*+x²))] = (K2) In[/=/= + 1/2 + √√( ²2 ) ² + y ² - 2²/2/2 + √√√( ²2 ) ² + y ² ] 3 y axis ↑(0,4/2) > _r=√x² + y² Di D *** 4/2 кадаг ду dy C 0 dep →→→x axis نیا
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