17. A rod AB of length L having charge density 2 = a(2L - x) where x is distance from end A and a is a constant then electric field at point P will be
Answers
Answer:
Let AB is the rod having L as its length. Let z is the distance from the middle of the rod. P is the point where electric field is to obtain. Let this distance is x.
The general expression for electric field is
E(P)=
4πε
0
1
line
∫
r
2
Q
∵λ=
L
Q
Q=CxL(given)
So, E(P)=
4πε
0
1
line
∫
r
2
CxL
Electric field at point P due to E1 and E2
E(P)=E
1
cosθ+E
2
cosθ
∵∣E
1
∣=∣E
2
∣=E
E(P)=2Ecosθ
E(P)=
4πε
0
1
0
∫
2
l
r
2
Cxdx
After solving the expression, the final electric field at point P is
E(P)=
4πε
0
1
z
z
2
+
4
L
2
CL
Explanation:
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Let AB is the rod having L as its length. Let z is the distance from the middle of the rod. P is the point where electric field is to obtain. Let this distance is x.
The general expression for electric field is
E(P)=
4πε
0
1
line
∫
r
2
Q
∵λ=
L
Q
Q=CxL(given)
So, E(P)=
4πε
0
1
line
∫
r
2
CxL
Electric field at point P due to E1 and E2
E(P)=E
1
cosθ+E
2
cosθ
∵∣E
1
∣=∣E
2
∣=E
E(P)=2Ecosθ
E(P)=
4πε
0
1
0
∫
2
l
r
2
Cxdx
After solving the expression, the final electric field at point P is
E(P)=
4πε
0
1
z
z
2
+
4
L
2
CL
Explanation: