Question

A very long uniform line of charge has charge per unit length
4.80 *μ*C/m and lies along the *x*-axis. A second
long uniform line of charge has charge per unit length -2.32
*μ*C/m and is parallel to the *x*-axis at *y*1
= 0.414 m .

Part A

What is the magnitude of the net electric field at point
*y*2 = 0.214 mon the *y*-axis?

Part B

What is the magnitude of the net electric field at point
*y*3 = 0.616 mon the *y*-axis?

Answer #1

A)

A line of charge having charge per unit length = p_{1} =
4.8 μC/m lies along the x-axis.

A second line of charge has charge per unit length =
p_{2}= -2.32 μC/m and is parallel to the x-axis at
y_{1}= 0.414m .

point y_{2}= 0.214 m on the y-axis

y_{2} is between the lines.As one is +ive and the other
is - ve, the field will be added up,it will be towards second -ve
line

E =2k[ p_{1}/r_{1} + p_{2}/r_{2}
]

E =2*9*10^{9}[ 4.8 *10^{-6}/0.214 +2.32
*10^{-6} /0.214 ]

E = 5.53*10^{5} N/C

The direction of the net electric field at point y_{2}=
0.214 m on the y-axis is along +y-axis

B) point y_{3}= 0.616 m on the y-axis

At y_{3}, the field are in opposite direction, the field
due to positive is less than field due to negative

Total field will be difference of two fields

E = 2k[ p_{1}/r_{1} -
p_{2}/r_{2} ]

E = 18*10^{3}[ 4.8 /0.616 - 2.32 /0.202]

E = -19.89*10^{4} N/C

The direction of the net electric field at point y_{3} =
0.616 m on the y-axis is -y-axis

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