Two infinitely long wire separated by a distance 5 m, carrying current I in opposite direction. If I = 10A, then the magnetic field intensity at point 'P' is

Concept:

The magnetic field intensity H due to an infinitely long straight current-carrying conductor at a distance r is given by:

\(H = \frac{I}{2\pi r} \text{ A/m}\)

Given:

• Current I = 10 A
• Distance between wires = 5 m
• Point P is 1 m away from the left wire and 4 m away from the right wire
• Currents are in opposite directions

Calculation:

Magnetic field at P due to the left wire:

H₁ = \(\frac{10}{2\pi \cdot 1} = \frac{10}{2\pi} = \frac{5}{\pi}\)A/m

Magnetic field at P due to the right wire:

H2 = \(\frac{10}{2\pi \cdot 4} = \frac{10}{8\pi} = \frac{5}{4\pi} \text{ A/m}\)

Since currents are in opposite directions, the magnetic fields will add up at point P (in the same direction due to the right-hand rule):

\(H = H_1 + H_2 = \frac{5}{\pi} + \frac{5}{4\pi} = \frac{20 + 5}{4\pi} = \frac{25}{4\pi} \text{ A/m}\)

Convert to match the options given (denominator \(8\pi\)):

\(H = \frac{25}{4\pi} = \frac{50}{8\pi} \text{ A/m}\)

Hence, the correct option is 1