intensity of electric field at point c in the given figure
Answers
Answer:
there is no figure
Explanation:
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Answer:
Consider an infinitesimal element as shown in figure (black) of length dx.
The amount of charge in the infinitesimal element is dq=λdx=αx dx
The distance between the charge element and the point is d+x.
Thus, the electric field due to the infinitesimal charge element is dE=
4πϵ
0
(d+x)
2
dq
=
4πϵ
0
(d+x)
2
αx
dx
Thus, the net electric field due to the rod is given by
E=∫dE=
0
∫
L
4πϵ
0
(d+x)
2
αx
dx=
4πϵ
0
α
0
∫
L
(d+x)
2
(d+x)−d
dx=
4πϵ
0
α
[
0
∫
L
d+x
1
dx+d
0
∫
L
−
(d+x)
2
1
dx]
0
∫
L
d+x
1
dx=[ln(d+x)]
0
L
=ln(d+L)−ln(d)=ln(1+
d
L
)
0
∫
L
−
(d+x)
2
1
dx=[
d+x
1
]
0
L
=
d+L
1
−
d
1
=−
d(d+L)
L
Thus, E=
4πϵ
0
α
[ln(1+
d
L
)−d(
d(d+L)
L
)]=
4πϵ
0
α
[ln(1+
d
L
)−
L+d
L
]
solution