Question

The magnitude of the magnetic field 100 cm from the axis of a long straight wire is 0.1g. calculate the current in the wire.

Answer 1

Given :

▪ Magnitude of magnetic field = 0.1G

▪ Distance = 100cm

To Find :

▪ Current flow in the wire.

Formula :

☞ Formula of magnetic field due to an infinitely long straight conducting wire is given by

$\bigstar\:\underline{\boxed{\bf{\red{B=\dfrac{\mu_o I}{2\pi a}}}}}$

• B denotes magnetic field
• I denotes current
• a denotes distance

Conversion :

✏ 1G = 10$^{-4}$T

✏ 0.1G = 10$^{-5}$T

✏ 100cm = 1m

Calculation :

$\dashrightarrow\sf\:B=\dfrac{\mu_o I}{2\pi a}\\ \\ \dashrightarrow\sf\:10^{-5}=\dfrac{4\pi\times 10^{-7}\times I}{2\pi \times 1}\\ \\ \dashrightarrow\sf\:I=\dfrac{10^{-5}}{2\times 10^{-7}}\\ \\ \dashrightarrow\sf\:I=0.5\times 10^2\\ \\ \dashrightarrow\underline{\boxed{\bf{\orange{I=50A}}}}\:\gray{\bigstar}$

Answer 2

Answer:

Magnitude of the magnetic field , B = 0.1 G = $\bold{10^{-5}\;T}$

Distance , a  = 100 cm = 1 m

$\bigstar\:\underline{\boxed{\bf{\red{B=\dfrac{\mu_o I}{2\pi a}}}}}$

$\bold{\implies 10^{-5}=\frac{4\pi *10^{-7} I}{2\pi *1} }\\\\\bold{\implies I = \frac{10^{-5}}{2*10^{-7}} \\\\}\\\\\bold{\implies I=\frac{100}{2} }\\\\\bold{\implies I=50 \;Amperes}$

$\bf{\blue{\bold{So , Current (I)\; in\; the\; wire = 50 Amperes}}}$