A current element of length dl and carrying current I in Z direction is placed at (1, 1, 0). Let magnetic field at origin be ${\vec{B}}_{1}$ and at point (2, 2, 0) be ${\vec{B}}_{2}$ , then which of the following is correct?

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$|{\vec{B}}_{1}| = |{\vec{B}}_{2}|$

${\vec{B}}_{1} = {\vec{B}}_{2}$

$|{\vec{B}}_{1}| = |2 {\vec{B}}_{2}|$

${\vec{B}}_{1} = - 2 {\vec{B}}_{2}$

answer is A.

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Detailed Solution

Magnitude of magnetic field will be same for both the points as they are located at equal distance from the wire. But the direction of magnetic field can be determined by right hand thumb rule.

By using right hand thumb rule, we can find the magnetic field lines would be counterclockwise circle in this case having center at O

Since and are two points that lie on a counterclockwise circle centered at, we can draw tangents to find magnetic field on both the points which will come out to be in opposite direction as can also be seen in the diagram.

$\begin{aligned} ∴ {\vec{B}}_{1} = - {\vec{B}}_{2} \\ \Rightarrow |{\vec{B}}_{1}| = |{\vec{B}}_{2}| \end{aligned}$