Ti 1. Magnetic Effect of Current

1. Current creates magnetic field

Whenever charges move, they produce a magnetic field $\mathbf{B}$. This discovery by Oersted in 1820 started the branch called electromagnetism.

2. Quantitative law – Biot–Savart

For a small current element $I\,d\mathbf{l}$ at a point $P$ in space, the magnetic field contribution is

Here $r$ is the distance from the element to $P$ and $\hat{\mathbf{r}}$ is the unit vector pointing from the element to $P$. Integrating $d\mathbf{B}$ over the whole conductor gives the total field.

3. Ampere’s Circuital Law

For cases with high symmetry, it is easier to use

where $I_{enc}$ is the current enclosed by the closed path. This directly gives $\mathbf{B}$ for long straight wires, solenoids and toroids.

4. Direction rules

• Right-Hand Thumb Rule (or Maxwell’s cork-screw rule) – gives field direction around straight wires.
• Right-Hand Coil Rule – if fingers curl in current direction in a solenoid, thumb gives magnetic north inside the coil.

5. Force due to magnetic field

Once the field exists, any other moving charge experiences a force $\mathbf{F}=q\,\mathbf{v}\times\mathbf{B}$. Two parallel current-carrying wires attract if currents are in same direction and repel otherwise, giving the operational definition of the ampere.

Logical flow to attack a numerical

1. Identify geometry (wire, loop, solenoid).
2. Decide between Biot–Savart (irregular shapes) or Ampere’s law (symmetry).
3. Use right-hand rule for direction.
4. Plug values, keep units (SI: $\mu_0 = 4\pi\times10^{-7}\,\text{T m A}^{-1}$).
5. Present answer with magnitude and direction.

🤔 What happens when electric current flows?

Imagine water flowing through a pipe. Now replace water with electric charges inside a wire. When these charges move, they behave like tiny marching magnets. Just like a bar-magnet pulls iron, the moving charges create an invisible magnetic field all around the wire.

🖐 How to know the field’s direction?

Take your right hand, point your thumb in the direction of current ($I$). Curl your fingers. Your fingers show the loops of the magnetic field. This is called the Right-Hand Thumb Rule.

🔍 Why is it useful?

Because with coils (called solenoids) we can make strong, switch-ON/OFF magnets (electromagnets) used in fans, loudspeakers and even in trains that float (maglev)!

Example Problem

Find magnetic field magnitude and direction at a point $5\,\text{cm}$ from an infinitely long straight wire carrying $8\,\text{A}$ current upwards.

Step 1: Identify formula

Because geometry is a straight, long wire, choose Ampere/ Biot–Savart result:

Step 2: Substitute values

Step 3: Direction (Right-Hand Thumb Rule)

Thumb up (current upwards) → fingers curl anticlockwise when viewed from above. At a point east of the wire, field points north.

Final Answer: