Question:
A straight long wire is carrying current I. The ratio of magnetic field due to this wire at perpendicular distance 2 cm and 5 cm respectively from the wire is
A straight long wire is carrying current I. The ratio of magnetic field due to this wire at perpendicular distance 2 cm and 5 cm respectively from the wire is
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B = mu0 I / (2 pi r), so B is inversely proportional to distance.
Updated On: Oct 1, 2026
- \(2:5\)
- \(3:5\)
- \(7:3\)
- \(5:2\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
The magnetic field around a long straight current-carrying wire decreases with distance. The field lines are circles around the wire.
Step 2: Key Formula or Approach:
\[ B = \frac{\mu_0I}{2\pi r} \Rightarrow B\propto\frac1r \]
Step 3: Detailed Explanation:
\[ \frac{B_1}{B_2} = \frac{r_2}{r_1} = \frac{5}{2} \]
Here \(r_1 = 2\) cm is the nearer point, so its field is larger. The ratio is 5:2.
Option (A) 2:5 is the inverse ratio and would be the answer if \(B\) were proportional to \(r\). Options (B) and (C) are not ratios of 2 and 5.
Final Answer:
The ratio is 5:2, option (D). \[ \boxed{5:2 \text{ (D)}} \]
The magnetic field around a long straight current-carrying wire decreases with distance. The field lines are circles around the wire.
Step 2: Key Formula or Approach:
\[ B = \frac{\mu_0I}{2\pi r} \Rightarrow B\propto\frac1r \]
Step 3: Detailed Explanation:
\[ \frac{B_1}{B_2} = \frac{r_2}{r_1} = \frac{5}{2} \]
Here \(r_1 = 2\) cm is the nearer point, so its field is larger. The ratio is 5:2.
Option (A) 2:5 is the inverse ratio and would be the answer if \(B\) were proportional to \(r\). Options (B) and (C) are not ratios of 2 and 5.
Final Answer:
The ratio is 5:2, option (D). \[ \boxed{5:2 \text{ (D)}} \]
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