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QPages 230-234: Q10: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q10 Solution: A wire of length carries a current along the -axis. A magnetic…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often mistakenly calculate the magnitude of the total magnetic field vector $B_0\sqrt{3}$ and multiply it by $il$, ignoring that only the component perpendicular to the current contributes to the force. Remember that the cross product $\hat{i} \times \hat{i} = 0$, so the parallel component $B_0\hat{i}$ must be discarded before computing the magnitude.

A wire of length

l

carries a current

i

along the

x

-axis. A magnetic field exists, which is given as

\vec{B} = B_0 \hat{i} + \hat{j} + \hat{k}) \text{ T}

. Find the magnitude of the magnetic force acting on the wire.

Step-by-Step Verified Solution

**Answer:**

F = i l B_0 \sqrt{2}

. **Step-by-Step Explanation:** Given:

\vec{B} = B_0 (\hat{i} + \hat{j} + \hat{k}) \text{ T}

, wire along x-axis with length

l

. The force

\vec{F} = i \vec{l} \times \vec{B} = i l \hat{i} \times B_0 (\hat{i} + \hat{j} + \hat{k}) = i l B_0 (\hat{k} - \hat{j})

. Magnitude

F = i l B_0 \sqrt{2}

.

All Questions in this Chapter

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