A long straight wire of circular cross-section (radius ) is carrying steady current . The current is uniformly distributed across this cross-section. The magnetic field is [2023]

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Q.
A long straight wire of circular cross-section (radius $a$ ) is carrying steady current $I$ . The current $I$ is uniformly distributed across this cross-section. The magnetic field is [2023]

Solution

Q.
A long straight wire of circular cross-section (radius $a$ ) is carrying steady current $I$ . The current $I$ is uniformly distributed across this cross-section. The magnetic field is [2023]

1 directly proportional to $r$ in the region $r < a$ and inversely proportional to $r$ in the region $r > a$

2 zero in the region $r < a$ and inversely proportional to $r$ in the region $r > a$

3 uniform in the region $r < a$ and inversely proportional to distance $r$ from the axis in the region $r > a$

4 inversely proportional to $r$ in the region $r < a$ and uniform throughout in the region $r > a$

Ans.
(1)

$B = {\begin{matrix} \frac{μ_{0} I r}{π a^{2}} & r \leq a \\ \frac{μ_{0} I}{π a^{2}} & r \geq a \end{matrix}$

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Solution

Q. A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is [2023]

1 directly proportional to r in the region r<a and inversely proportional to r in the region r>a

2 zero in the region r<a and inversely proportional to r in the region r>a

3 uniform in the region r<a and inversely proportional to distance r from the axis in the region r>a

4 inversely proportional to r in the region r<a and uniform throughout in the region r>a

Ans. (1) B={μ0Irπa2r≤aμ0Iπa2r≥a

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Q.
A long straight wire of circular cross-section (radius $a$ ) is carrying steady current $I$ . The current $I$ is uniformly distributed across this cross-section. The magnetic field is [2023]

1 directly proportional to $r$ in the region $r < a$ and inversely proportional to $r$ in the region $r > a$

2 zero in the region $r < a$ and inversely proportional to $r$ in the region $r > a$

3 uniform in the region $r < a$ and inversely proportional to distance $r$ from the axis in the region $r > a$

4 inversely proportional to $r$ in the region $r < a$ and uniform throughout in the region $r > a$

Ans.
(1)

$B = {\begin{matrix} \frac{μ_{0} I r}{π a^{2}} & r \leq a \\ \frac{μ_{0} I}{π a^{2}} & r \geq a \end{matrix}$