Question:
Magnetic field at $0.1\text{ m}$ from a long straight wire carrying $10\text{ A}$ current is:
Magnetic field at $0.1\text{ m}$ from a long straight wire carrying $10\text{ A}$ current is:
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For any long straight wire, the field formula can be written as $B = \frac{2 \times 10^{-7} \times I}{r}$.
Using powers of ten directly prevents arithmetic mistakes in competitive exams.
Using powers of ten directly prevents arithmetic mistakes in competitive exams.
Updated On: Jul 22, 2026
- $2 \times 10^{-5}\text{ T}$
- $2 \times 10^{-4}\text{ T}$
- $2 \times 10^{-6}\text{ T}$
- $10^{-5}\text{ T}$
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
We need to calculate the magnetic field induction $B$ at a specified perpendicular distance from a long, straight conducting wire carrying a known electric current.
Step 2: Key Formula and Approach:
By Ampere's Circuital Law, the magnetic field $B$ at a distance $r$ from an infinitely long straight wire carrying current $I$ is:
\[ B = \frac{\mu_0 I}{2\pi r} \] where $\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}$ is the permeability of free space.
Step 3: Detailed Explanation:
• Identify given parameters:
Current $I = 10\text{ A}$
Perpendicular distance $r = 0.1\text{ m}$
• Calculate the magnetic field ($B$):
Substitute the parameters into the formula:
\[ B = \frac{\mu_0 I}{2\pi r} \] Since $\frac{\mu_0}{2\pi} = 2 \times 10^{-7}\text{ T m A}^{-1}$:
\[ B = \left(2 \times 10^{-7}\right) \times \frac{I}{r} \] \[ B = \left(2 \times 10^{-7}\right) \times \frac{10}{0.1} \] \[ B = \left(2 \times 10^{-7}\right) \times 100 \] \[ B = 2 \times 10^{-5}\text{ T} \]
Step 4: Final Answer:
The magnetic field at a distance of $0.1\text{ m}$ is $2 \times 10^{-5}\text{ T}$, which corresponds to Option (A).
We need to calculate the magnetic field induction $B$ at a specified perpendicular distance from a long, straight conducting wire carrying a known electric current.
Step 2: Key Formula and Approach:
By Ampere's Circuital Law, the magnetic field $B$ at a distance $r$ from an infinitely long straight wire carrying current $I$ is:
\[ B = \frac{\mu_0 I}{2\pi r} \] where $\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}$ is the permeability of free space.
Step 3: Detailed Explanation:
• Identify given parameters:
Current $I = 10\text{ A}$
Perpendicular distance $r = 0.1\text{ m}$
• Calculate the magnetic field ($B$):
Substitute the parameters into the formula:
\[ B = \frac{\mu_0 I}{2\pi r} \] Since $\frac{\mu_0}{2\pi} = 2 \times 10^{-7}\text{ T m A}^{-1}$:
\[ B = \left(2 \times 10^{-7}\right) \times \frac{I}{r} \] \[ B = \left(2 \times 10^{-7}\right) \times \frac{10}{0.1} \] \[ B = \left(2 \times 10^{-7}\right) \times 100 \] \[ B = 2 \times 10^{-5}\text{ T} \]
Step 4: Final Answer:
The magnetic field at a distance of $0.1\text{ m}$ is $2 \times 10^{-5}\text{ T}$, which corresponds to Option (A).
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