Question

A current i is flowing in a straight conductor of length l the magnetic induction at a point distance l y format centre will be

Answer 1

It is based on the phenomenon of the biot-savart's law.

• The magnetic field lines due to the straight conductor carrying current are in the form of concentric circles with the conductor as centre.
• They are lying in a plane perpendicular to the straight conductor.
• The Right hand thumb rule or maxwell's cork screw rule.
• This shows the direction of the magnetic field around the current carrying wire.

Answer 2

Complete question:

A current i is flowing in a straight conductor of length L. The magnetic induction at a point distant L/4 from its center will be-

Answer:

The magnetic induction at a point is 4μ₀i/√5πL

Explanation:

The Biot savart Law is applied here,

B = μ₀i/4πR (sin θ₁ + sin θ₂)

Now,

sin θ₁ = (L/2)/√((L/2)²+(L/2)²)

sin θ₁ = 1/(2√(1/4+1/16))

∴ sin θ₁ = 4/(2√5)

Now,

sin θ₂ = (L/2)/√((L/2)²+(L/2)²)

sin θ₂ = 1/(2√(1/4+1/16))

∴ sin θ₂ = 4/(2√5)

Now, the magnetic induction is:

B = μ₀i/4π(L/4) × 2 (4/(2√5))

B = μ₀i/π(L/4) × 1/√5

∴ B = 4μ₀i/√5πL