Question

. Magnetic field at point P due to both infinite long current
carrying wires ​

Answer 1

Answer:

2

Due to infinite long wire magnetic field at distance r

$= \frac{ \mu</strong><strong>_</strong><strong>0</strong><strong>I</strong><strong>}{2\pi r}$

So due to both wires

$\frac{ \mu</strong><strong>_</strong><strong>0 \times 5}{2\pi} ( \frac{1}{</strong><strong>7</strong><strong>.</strong><strong>5} )+ \frac{ \mu</strong><strong>_</strong><strong>0 \times 2.5}{2\pi} \frac{1}{</strong><strong>2</strong><strong>.5} \\ \\ = \frac{ \mu</strong><strong>_</strong><strong>0}{2\pi}( \frac{2 + 3}{3} ) \\ \\ = \frac{ 5\mu</strong><strong>_</strong><strong>0}{6\pi}$

For direction use Right thumb , fingers in direction of current and bend them towards point it will be in the plane .

Answer 2

The magnetic field at point P due to both infinite long current  carrying wires ​is $\dfrac{5\mu_{0}}{6\pi}$

(2) option is correct.

Explanation:

Given that,

Current in wire 1 = 5 A

Current in wire 2 = 2.5 A

Distance between wires = 5 m

Distance between second wire and point P = 2.5 m

We need to calculate the magnetic field due to first wire

Using formula of magnetic field

$B_{1} = \dfrac{\mu_{0}I}{2\pi r}$

Where, r = distance

I = current

Put the value into the formula

$B_{1}=\dfrac{\mu_{0}\times5}{2\pi\times(5+2.5)}$

$B_{1}=\dfrac{5\mu_{0}}{15\pi}$

We need to calculate the magnetic field due to second wire

Using formula of magnetic field

$B_{2} = \dfrac{\mu_{0}I}{2\pi r}$

Put the value into the formula

$B_{2}=\dfrac{\mu_{0}\times2.5}{2\pi\times2.5}$

$B_{2}=\dfrac{\mu_{0}}{2\pi}$

We need to calculate the magnetic field due to both infinite long current

$B = B_{1}+B_{2}$

$B=\dfrac{5\mu_{0}}{15\pi}+\dfrac{\mu_{0}}{2\pi}$

$B=\dfrac{5\mu_{0}}{6\pi}$

Hence, The magnetic field at point P due to both infinite long current  carrying wires ​is $\dfrac{5\mu_{0}}{6\pi}$

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Topic : magnetic field

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