A straight wire of finite length carrying current i subtends an angle of 60 at point P as shown. The magnetic field at P is?
Answers
Answer: modulus of dB = (μ0 / 4π) × (Idl sin60 / r2)
Explanation:
A small quantity of current carrying through a conductor length of length dl also carrying a current I gives an elementary source of magnetic field. The force exerted on an another similar conductor will be expressed in terms of magnetic field dB as due to the first. The dependence of magnetic field dB on the current I will be on the size that's length and alignment of the length element dl and on a certain distance .
Consider a wire carrying a current I in a specific direction .For a small element of the wire of length dl. The direction of this element will be along to that of current so that it can form a vector Idl. If we want to know the magnetic field produced at a point of P which is provided due to this small element, then we can use the Biot-Savart’s Law.
The magnitude of the magnetic field dB at a distance r from a current carrying element or conductor of length dl is found as directly proportional to I and to the length dl. And is inversely proportional to the square of the distance modulus of r. The direction of the Magnetic Field is set to be perpendicular to the line element dl as well as to the radius r.
Thus the vector notation is given as,
dB = u0 x Idl × r / r³
= (μ0 / 4π ) × (Idl × r / r3),
where μ0/4π is a constant of permeability. The above expression holds good when the medium is entirely vacuum. Therefore the magnitude of this field at point p is
|dB| = (μ0 / 4π) × (Idl sin60 / r2)