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QPages 249-253: Q43: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q43 Solution: A circular loop of radius carries a current . How should a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often confuse the magnetic field at the centre of a circular loop with the field of a straight wire, using $B_{ ext{loop}}=rac{mu_0 I}{2pi r}$ instead of the correct $B_{ ext{loop}}=rac{mu_0 I}{2r}$. They also mistakenly identify the distance from the wire to the centre as the loop radius $r$ rather than the variable $d$. Always use $B_{ ext{loop}}=rac{mu_0 I}{2r}$ and set $d$ equal to the actual separation between the wire and the loop centre when equating the two fields.

A circular loop of radius

r

carries a current

i

. How should a long, straight wire carrying a current

4i

be placed in the plane of the circle so that the magnetic field at the centre becomes zero?

Step-by-Step Verified Solution

**Answer:** The wire should be placed at a distance

r = R/2

from the centre, parallel to the plane of the loop, with current

4i

. **Step-by-Step Explanation:** Field due to loop at centre:

B_1 = \frac{\mu_0 i}{2r}

. Field due to straight wire:

B_2 = \frac{\mu_0 \times 4i}{2\pi d}

. For zero:

\frac{\mu_0 i}{2r} = \frac{\mu_0 \times 4i}{2\pi d} \Rightarrow d = \frac{4r}{\pi}

.

All Questions in this Chapter

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