Question

A long straight conductor carries a current of \(10\,\text{A}\). The magnetic field at a point \(20\,\text{cm}\) away from the conductor is \((\mu_0=4\pi\times10^{-7}\,\text{TmA}^{-1})\)

• A. \(1\times10^{-5}\,\text{T}\)
• B. \(2\times10^{-5}\,\text{T}\)
• C. \(5\times10^{-6}\,\text{T}\)
• D. \(4\times10^{-5}\,\text{T}\)

Hint:

Magnetic field due to a long straight wire: \[ \boxed{B=\frac{\mu_0 I}{2\pi r}} \] Important observations: \[ B\propto I \] \[ B\propto \frac{1}{r} \] Doubling the distance halves the magnetic field.

Answer 1

The Correct Option is A

Step 1: Recall the magnetic field due to a long straight conductor. \[ B=\frac{\mu_0 I}{2\pi r} \] Given: \[ I=10\,\text{A} \] \[ r=20\,\text{cm}=0.2\,\text{m} \]

Step 2: Substitute the values. \[ B= \frac{(4\pi\times10^{-7})(10)} {2\pi(0.2)} \] \[ B= \frac{4\times10^{-6}} {0.4} \] \[ B=1\times10^{-5}\,\text{T} \]

Step 3: Identify the correct option. \[ \boxed{B=1\times10^{-5}\,\text{T}} \] Therefore, \[ \boxed{\text{(A)}} \] is the correct answer.