Moving Charges and Magnetism

Answer

The magnetic field $ \Delta B $ at a point due to a small current element $ \Delta l $ is given by: $$ |\Delta B| = \frac{\mu_0}{4\pi} \frac{I \Delta l \sin\theta}{r^2} $$ Where: - $ \mu_0 $ = perme…

Answer

Given: - $ I = 5 \, \text{A} $ - $ r = 10 \, \text{cm} = 0.1 \, \text{m} $ Formula: $$ B = \frac{\mu_0 I}{2\pi r} $$ Step 1: Substitute values $$ B = \frac{4\pi \times 10^{-7} \times 5}{2\pi \times …

Answer

A current-carrying wire produces a magnetic field around it (Oersted’s discovery). This magnetic field interacts with the magnetic needle, exerting a torque that aligns the needle along the net magnet…

Answer

This formula gives the magnetic field at the **center** of a **circular coil** of radius $ r $ carrying current $ I $. Steps: 1. Ensure the point is at the center of the loop. 2. Use $ B = \frac{\mu_…

Answer

Consider a circular loop of radius $ r $ carrying current $ I $. From Biot-Savart’s law: $$ |\Delta B| = \frac{\mu_0}{4\pi} \frac{I \Delta l \sin\theta}{r^2} $$ At center, $ \theta = 90^\circ \Right…

Answer

The line integral of magnetic field $ \vec{B} $ around any closed path is equal to $ \mu_0 $ times the total current $ I $ enclosed by the path: $$ \oint \vec{B} \cdot d\vec{l} = \mu_0 I $$ Where: -…

Answer

Consider a long straight wire carrying current $ I $. Draw an Amperian loop: circle of radius $ r $ around wire. By symmetry, $ B $ is constant and tangential at all points on loop. $$ \oint \vec{B…

Answer

Given: - Length $ L = 40 \, \text{cm} = 0.4 \, \text{m} $ - Number of turns $ N = 400 $ - Current $ I = 3 \, \text{A} $ Turns per unit length: $$ n = \frac{400}{0.4} = 1000 \, \text{turns/m} $$ Form…