Solved Examples: Finding Magnetic Field Strength from Current

📚 Quick Study Guide

• 🧲 The magnetic field strength (B) around a current-carrying wire is measured in Tesla (T).
• 📏 Biot-Savart Law helps calculate the magnetic field due to a small current element: $d\vec{B} = \frac{\mu_0}{4\pi} \frac{Id\vec{l} \times \hat{r}}{r^2}$, where $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} T \cdot m/A$).
• 🧭 Ampere's Law simplifies calculations for symmetrical current distributions: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$.
• 💡 Magnetic field due to a long straight wire: $B = \frac{\mu_0 I}{2\pi r}$, where $r$ is the distance from the wire.
• 🌀 Magnetic field inside a solenoid: $B = \mu_0 n I$, where $n$ is the number of turns per unit length.
• 🍩 Magnetic field at the center of a circular loop: $B = \frac{\mu_0 I}{2R}$, where $R$ is the radius of the loop.

🧪 Practice Quiz

1. What is the magnetic field strength at a distance of 2 cm from a long straight wire carrying a current of 10 A?
   1. 2 x 10^-5 T
   2. 1 x 10^-4 T
   3. 3 x 10^-5 T
   4. 4 x 10^-5 T
2. A solenoid with 500 turns per meter carries a current of 2 A. What is the magnetic field inside the solenoid?
   1. 1.26 x 10^-3 T
   2. 2.51 x 10^-3 T
   3. 3.77 x 10^-3 T
   4. 5.03 x 10^-3 T
3. A circular loop of radius 5 cm carries a current of 5 A. What is the magnetic field at the center of the loop?
   1. 6.28 x 10^-5 T
   2. 3.14 x 10^-5 T
   3. 1.57 x 10^-4 T
   4. 7.85 x 10^-5 T
4. What is the effect on the magnetic field strength if the current in a wire is doubled?
   1. The magnetic field strength is halved.
   2. The magnetic field strength remains the same.
   3. The magnetic field strength is doubled.
   4. The magnetic field strength is quadrupled.
5. A wire carries a current perpendicular to a magnetic field. What is the direction of the force on the wire?
   1. Parallel to the magnetic field
   2. Opposite to the magnetic field
   3. Perpendicular to both the current and the magnetic field
   4. Along the direction of the current
6. If the number of turns per unit length of a solenoid is doubled, what happens to the magnetic field inside?
   1. It is halved.
   2. It remains the same.
   3. It is doubled.
   4. It is quadrupled.
7. What is the magnetic field strength very far away from a finite length current carrying wire?
   1. It approaches infinity.
   2. It approaches zero.
   3. It remains constant.
   4. It oscillates.