The magnetic field at a point at a distance r from the current element is proportional to:-. (a). r , (b). r^2 , (c). 1/r , (d). 1/r^2
Answers
Answer:
A current carrying wire generates a magnetic field. According to Biot-Savart’s law, the magnetic field at a point due to an element of a conductor carrying current is,
Directly proportional to the strength of the current, i
Directly proportional to the length of the element, dl
Directly proportional to the Sine of the angle θ between the element and the line joining the element to the point and
Inversely proportional to the square of the distance r between the element and the point.
d
B
=
4π
μ
0
i
r
3
d
l
×
r
Answer:
option c is correct
The magnetic field at a point at a distance r from the current element is inversely proportional to r
Explanation:
The wire is taken into consideration to be a cylindrical Gaussian surface. This is due to the fact to determine the electric field (E)
at point P Gauss law is used.
The surface location of the curved part is given as:
S = 2πrl
The overall charge enclosed via way of means of the Gaussian surface is given as:
q = λl
The electric-powered flux through the give-up surfaces of the cylindrical Gaussian surface is given as:
Φ1 = 0
The electric-powered flux through the curved surface of the cylindrical Gaussian surface is given as:
Φ2 = E cosθ.s
Φ2 = E x 1 x 2πrl
The overall electric-powered flux is given as:
Φ = Φ1 + Φ2
Φ = 0 + E cosθ.s
Φ2 = 2πrlE (eq. 1)
From Gauss regulation, we recognize that
ϕ = q / ε₀ ⇒ λl / ε₀
(eq.2)
From eq 1. And eq 2
2πrlE = λl / ε₀
E = λ / 2πε₀r
Therefore, the above equation is the electrical area because of an infinitely long straight uniformly charged wire.
so,
B= μ₀I / 2πr
⟹ B∝ 1/r
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