Question

A current of $1 A$ is flowing along positive $x-a x i s$ through a straight wire of length $0.5\, m$ placed in a region of a magnetic field given by $\vec{B}=(2 \hat{i}+4 \hat{j}) T$. The magnitude and the direction of the force experienced by the wire respectively are

• A. $\sqrt{18}N$, along positive z-axis
• B. $\sqrt{20}N$, along positive x-axis
• C. 2N, along positive z-axis
• D. 4N, along positive y-axis

Answer 1

Answer: (C)

The force experienced by the wire placed in magnetic field, $F=B i l$
$=(2 \hat{ i }+4 \hat{ j })\left(1 \hat{ i } \times \frac{1}{2}\right) $
$=\hat{ i } \times \hat{ i }+4 \times \frac{1}{2}(\hat{ i } \times \hat{ j })=2 \hat{ k } N$
Direction of this force can be find out by Fleming's left hand rule which is along pasitive z-axis.