An infinitely long straight wire carries a current of 10 A. At... | General Science MCQ | Examoogle

General SciencePhysics

An infinitely long straight wire carries a current of 10 A. At what distance r from the wire is the magnetic field 4 $\times 10$ ⁻⁵ T?

0.02 m

0.05 m

0.1 m

0.2 m

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics

Option B

0.05 m

Quick Summary:

The magnetic field produced by an infinitely long straight wire is inversely proportional to the perpendicular distance from the wire. Using the Biot-Savart Law application for an infinite wire, the distance $r$ is calculated to be 0.05 m given the current of 10 A and the field strength of $4 \times 10^{-5} \text{ T}$ .

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of the magnetic field as ripples in a pond spreading out from a stick held vertically in the water; the further you move away from the stick, the weaker the ripples become.

🔢 Key Formulas

$B = \frac{\mu_{0} I}{2 \pi r}$ — Magnetic field of an infinitely long straight wire

$r = \frac{\mu_{0} I}{2 \pi B}$ — Rearranged formula to calculate distance

⚙️ Working Principle

The magnetic field $B$ around a straight current-carrying conductor is determined by the Ampere's circuital law and the Biot-Savart law. The relationship is expressed as $B = \frac{\mu_{0} I}{2 \pi r}$ , where $\mu_{0}$ is the permeability of free space ( $4 \pi \times 10^{-7} \text{ T m/A}$ ), $I$ is the current, and $r$ is the radial distance.

📌 Key Points

▸
The magnetic field is directly proportional to the current $I$ flowing through the wire.
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The magnetic field is inversely proportional to the distance $r$ from the wire.
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The field lines form concentric circles around the conductor as per the Right-Hand Thumb Rule.

✅ Advantages

▸
Simple mathematical relationship for design of electromagnetic components.

❌ Disadvantages / Limitations

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The formula assumes the wire is infinitely long, which is an idealization.

🛠️ Applications / Uses

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Design of electromagnets
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Measurement of currents using Hall effect sensors

📄 Additional Information

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Permeability of free space $\mu_{0} = 4 \pi \times 10^{-7} \text{ T m/A}$ .
▸
Calculation: $r = \frac{(4 \pi \times 10^{-7}) \times 10}{2 \pi \times 4 \times 10^{-5}} = \frac{2 \times 10^{-6}}{4 \times 10^{-5}} = 0.5 \times 10^{-1} = 0.05 \text{ m}$ .

📊 Diagram / Illustration

✅

B is correct — Using the formula $B = \frac{\mu_{0} I}{2 \pi r}$ , the calculated distance for $B = 4 \times 10^{-5} \text{ T}$ and $I = 10 \text{ A}$ is $0.05 \text{ m}$ .

Core Concepts Used

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Biot-Savart Law Electromagnetism Ampere's Circuital Law

💡 EXAM TIP

Always ensure units are in SI (Tesla, Amperes, Meters) before plugging values into the formula to avoid errors in powers of ten.

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