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

General SciencePhysics: Electricity and Magnetism

An infinitely long straight wire carries a current of I. At what distance r from the wire is the magnetic field 5 × 10 ⁻ ⁶ T if I = 15 A?

0.6 m

0.3 m

7.5 m

3 m

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity and Magnetism

Option A

0.6 m

Quick Summary:

The magnetic field produced by an infinitely long straight wire carrying a current is determined by the Biot-Savart Law. For a current of $I = 15\, \text{A}$ and a magnetic field $B = 5 \times 10^{-6}\, \text{T}$ , the distance $r$ is calculated as $0.6\, \text{m}$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of the magnetic field like a whirlpool forming around a stick being dragged through water; the further away you stand from the stick, the weaker the swirling effect becomes.

🧠 Memory Mnemonic / Shortcut Aid

B-I-R: 'Big Interests Require Radiant' distance (B, I, r relationship).

🔢 Key Formulas

$B = \frac{\mu_0 I}{2 \pi r}$ — Biot-Savart Law for a straight wire

$r = \frac{\mu_0 I}{2 \pi B}$ — Rearranged formula to find distance

⚙️ Working Principle

The magnetic field $B$ around a straight current-carrying conductor follows Ampere's Law, resulting in the formula $B = \frac{\mu_0 I}{2 \pi r}$ . Here, $\mu_0$ is the permeability of free space ( $4 \pi \times 10^{-7}\, \text{T m/A}$ ). Rearranging for distance gives $r = \frac{\mu_0 I}{2 \pi B}$ . Substituting values: $r = \frac{(4 \pi \times 10^{-7}) \times 15}{2 \pi \times 5 \times 10^{-6}} = \frac{2 \times 10^{-7} \times 15}{5 \times 10^{-6}} = \frac{30 \times 10^{-7}}{5 \times 10^{-6}} = 6 \times 10^{-1} = 0.6\, \text{m}$ .

📌 Key Points

▸
The magnetic field is inversely proportional to the distance from the wire ( $B \propto \frac{1}{r}$ ).
▸
The magnetic field is directly proportional to the current flowing through the wire ( $B \propto I$ ).
▸
Permeability of free space $\mu_0 = 4 \pi \times 10^{-7}\, \text{T m/A}$ is a fundamental constant.

✅ Advantages

▸
Predictable magnetic field distribution allows for accurate design of electromagnetic components.

❌ Disadvantages / Limitations

▸
Assumes an 'infinitely' long wire, which is an idealization; short wires require complex integration (Biot-Savart Law).

🛠️ Applications / Uses

▸
Designing high-voltage transmission line shielding.
▸
Calibration of magnetic sensors (Hall effect sensors).

📄 Additional Information

▸
The value of $\mu_0$ is exactly $4 \pi \times 10^{-7}\, \text{T m/A}$ .
▸
Option B (0.3 m) would result in a magnetic field of $10 \times 10^{-6}\, \text{T}$ .

📊 Diagram / Illustration

✅

A is correct — The distance is calculated to be 0.6 m using the Biot-Savart formula for a long straight current-carrying wire.

Core Concepts Used

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Biot-Savart Law Electromagnetism Magnetic field of straight wire

💡 EXAM TIP

Always ensure current is in Amperes and distance in meters; if given in cm or mA, convert to SI units before calculating to avoid magnitude errors.

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