A straight wire carries a current of 10 A. What is the magnetic field at a distance of 0.2 m from the wire? (G

Question

A straight wire carries a current of 10 A. What is the magnetic field at a distance of 0.2 m from the wire? (Given $\mu_{0} = 4\pi 	imes 10^{-7}$ T.m/A)

Examoogle · Accepted Answer

The correct answer is Option A: $1 	imes 10^{-5} 	ext{ T}$. The magnetic field produced by a long straight current-carrying wire is directly proportional to the current and inversely proportional to the perpendicular distance from the wire. Using the formula $B = \frac{\mu_{0}I}{2\pi r}$, we calculate the field to be $1 	imes 10^{-5} 	ext{ T}$.

Step-by-Step Solution & Concepts:
The magnetic field produced by a long straight current-carrying wire is directly proportional to the current and inversely proportional to the perpendicular distance from the wire. Using the formula $B = \frac{\mu_{0}I}{2\pi r}$, we calculate the field to be $1 	imes 10^{-5} 	ext{ T}$.

Working Principle: According to the Biot-Savart law or Ampere's circuital law, a moving charge (electric current) creates a magnetic field in the surrounding space. For an infinitely long straight wire, the field lines form concentric circles around the conductor, with the field strength $B$ determined by the current $I$ and distance $r$. The constant $\mu_{0}$ is the permeability of free space.

Key Formulas: $B = \frac{\mu_{0}I}{2\pi r}$ — Magnetic field of a long straight wire; $I = 10 	ext{ A}, \quad r = 0.2 	ext{ m}, \quad \mu_{0} = 4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}$ — Given variables

Key Points: The magnetic field is always perpendicular to the direction of current flow.; Magnetic field lines for a straight wire are always circular.; SI unit of magnetic field is Tesla (T).

Advantages: Predictable field geometry; Easy to manipulate by varying current

Disadvantages: Strength drops rapidly with distance; Requires high current for significant field strength at a distance

Applications: Electromagnets; Transmission line cables

Additional Info: Calculation: $B = \frac{(4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}) 	imes 10 	ext{ A}}{2\pi 	imes 0.2 	ext{ m}} = \frac{2 	imes 10^{-6}}{0.2} = 1 	imes 10^{-5} 	ext{ T}$.. Option B is incorrect because it uses an incorrect radius or constant calculation, Option C and D are mathematical errors.

Answer: A is correct — The calculated magnetic field is $1 	imes 10^{-5} 	ext{ T}$ using the Biot-Savart derived formula for an infinite wire.

Exam Tip: Always ensure the current is in Amperes and distance is in meters before applying the formula to avoid unit mismatch errors.

Examoogle · Answer

Option B: $2 	imes 10^{-5} 	ext{ T}$

Examoogle · Answer

Option C: $5 	imes 10^{-6} 	ext{ T}$

Examoogle · Answer

Option D: $1 	imes 10^{-6} 	ext{ T}$

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