Question

If the magnetic field at a distance of 2 cm from an infinite current carrying wire is 10-6 weber/m2, then the value of current in ampere will be:​

Answer 1

ANSWER:

• The value of current = 10 A.

GIVEN:

• Magnetic field from an infinite current carrying wire is 10⁻⁶ weber/m².

• Distance is 2 cm.

TO FIND:

• The value of current in Ampere.

EXPLANATION:

$\boxed{ \bold{ \large{ \gray{B = \dfrac{\mu_oI}{4\pi a}(sin \ \phi_1 + sin \ \phi_{2} )}}}}$

The above formula is for calculating magnetic field around a thin straight current carrying conductor.

$\sf For\ a\ infinite\ wire,\ \phi_1 = \phi_2=90^{\circ}$

$\sf B = \dfrac{\mu_oI}{4\pi a}(sin \ {90}^{ \circ} + sin \ {90}^{ \circ} )$

$\sf B= \dfrac{\mu_oI}{4\pi a}(1 + 1 )$

$\sf B = \dfrac{\mu_oI}{4\pi a}(2)$

$\boxed{ \bold{ \large{ \gray{ B = \dfrac{\mu_oI}{2\pi a}}}}}$

The above formula is for calculating magnetic field around a thin straight current carrying conductor of infinite length.

$\sf B = 10^6 \ weber\ m^{-2}$

$\sf a = 2 \ cm = 2\times 10^{-2}\ m$

$\sf \mu_o = 4 \pi \times {10}^{ - 7} \ T\ m \ A^{-1}$

$\sf 10^6= \dfrac{(4\pi \times {10}^{ - 7})I}{2\pi (2\times 10^{-2})}$

$\sf 10^6= \dfrac{(2\times {10}^{ - 7})I}{(2\times 10^{-2})}$

$\sf 10^6= \dfrac{( {10}^{ - 7})I}{( 10^{-2})}$

$\sf 10^6= ( {10}^{ 5})I$

$\sf \dfrac{10^6}{ {10}^{ 5}} = I$

$\sf I = 10\ A$

HENCE THE VALUE OF CURRENT = 10 A.