An element is placed at the origin and carries a large current = 10 A. The magnetic field on the y-axis at a distance of 0.5 m from the element of 1 cm length is

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Solution

Q.
An element $∆ l = ∆ x \hat{i}$ is placed at the origin and carries a large current $I$ = 10 A. The magnetic field on the y-axis at a distance of 0.5 m from the element $∆ x$ of 1 cm length is ______. [2024]

1 $8 \times 10^{- 8} T$

2 $10 \times 10^{- 8} T$

3 $4 \times 10^{- 8} T$

4 $12 \times 10^{- 8} T$

Ans.
(3)

By Biot-Savart law, $\vec{d B} = \frac{μ_{0} i}{4 π} \frac{(\vec{d l} \times \vec{r})}{r^{3}} (Tesla)$

Since element is very small,

Given: $\vec{d l} = \frac{1}{100} \hat{i} m, \vec{r} = \frac{1}{2} \hat{j} m, i = 10 A, θ = 90 °$

$= 10^{- 7} \times 10 \times \frac{(\frac{1}{100} \hat{i} \times \frac{1}{2} \hat{j})}{{(\frac{1}{2})}^{3}}$

$= 10^{- 7} \times 10 \times \frac{8}{200} \hat{k} = 4 \times 10^{- 8} T (+ \hat{k})$

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