Physics · Moving Charges and Magnetic Field

JEE Advanced 2024 — Paper 1 — Question 19

An infinitely long wire, located on the z-axis, carries a current I along the +z-direction and produces the magnetic field $\overrightarrow{\mathrm{B}}$ . The magnitude of the line integral $\int \overrightarrow{\mathrm{B}} . \overrightarrow{\mathrm{d} l}$ along a straight line from the point $(-\sqrt{3} a, a, 0)$ to $(a, a, 0)$ is given by[0pt] [ $\mu_{0}$ is the magnetic permeability of free space.]

Option A:
$7 \mu_{0} / / 24$
Correct
Option B:
$7 \mu_{0} \mathrm{I} / 12$
Option C:
$\mu_{0} I / 8$
Option D:
$\mu_{0} I / 6$

Answer: A

Step-by-step solution

$\oint \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{d} \ell}=\int_{0}^{\mathrm{i}} \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{d} \ell}+\int_{\mathrm{i}}^{\mathrm{f}} \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{d} \ell}+\int_{\mathrm{f}}^{0} \overrightarrow{\mathrm{~B}} \cdot \overrightarrow{\mathrm{~d} \ell}=\mu_{0} \frac{\mathrm{I}}{2 \pi} \frac{7 \pi}{12}$ So, $\int_{\mathrm{i}}^{\mathrm{f}} \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{d} \ell}=\frac{7 \mu_{0} \mathrm{I}}{24}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2024
Paper: Paper 1
Subject: Physics
Chapter: Moving Charges and Magnetic Field
Topic: Ampère's Law and its Applications