### Force And Torque Due To Magnetic Field

**Concepts to Remember for the “Force and Torque Due to Magnetic Field”:**

**1. Magnetic field due to a current-carrying wire:**

- Visualize the magnetic field lines around a current-carrying wire using the right-hand thumb rule.
- Remember the inverse square law: The strength of the magnetic field decreases as the square of the distance from the wire increases.

**2. Magnetic field due to a solenoid:**

- Imagine a solenoid as a tightly packed coil of wire.
- The magnetic field inside a solenoid is uniform and its strength depends on the number of turns, current, and length of the solenoid.

**3. Magnetic field due to a moving charge:**

- Visualize the magnetic field lines around a moving charge using the right-hand rule.
- Remember that the magnetic field strength is directly proportional to the velocity of the charge and the magnetic permeability of the medium.

**4. Lorentz force acting on a moving charge in a magnetic field:**

- The Lorentz force is a vector sum of the electric and magnetic forces acting on a moving charge in a magnetic field.
- Remember the equation for the Lorentz force: $\overrightarrow{F} = q(\overrightarrow{E} + \overrightarrow{v} \times \overrightarrow{B})$ where $q$ is the charge, $\overrightarrow{E}$ is the electric field, $\overrightarrow{v}$ is the velocity, and $\overrightarrow{B}$ is the magnetic field.

**5. Torque acting on a current loop in a magnetic field:**

- Imagine a current loop as a closed loop of wire carrying current.
- The torque acting on a current loop in a magnetic field tends to align the loop with the field.
- Remember the equation for the torque: $\overrightarrow{\tau} = \overrightarrow{m} \times \overrightarrow{B}$ where $\overrightarrow{\tau}$ is the torque, $\overrightarrow{m}$ is the magnetic moment, and $\overrightarrow{B}$ is the magnetic field.

**6. Magnetic moment of a current loop:**

- The magnetic moment of a current loop is a measure of its strength and orientation as a magnet.
- It depends on the current flowing through the loop and the area enclosed by the loop.

**7. Conditions for equilibrium of a current loop in a magnetic field:**

- A current loop is in equilibrium when the net torque acting on it is zero.
- This condition is achieved when the magnetic moment of the loop is aligned with the magnetic field.

**8. Ferromagnetism, paramagnetism, and diamagnetism:**

- Ferromagnetic materials are strongly attracted to magnets, paramagnetic materials are weakly attracted, and diamagnetic materials are repelled.
- These behaviors arise due to the alignment or opposition of the magnetic moments of the atoms within the materials.

**9. Hysteresis curve:**

- A hysteresis curve shows the relationship between the magnetic field strength and the magnetization of a ferromagnetic material.
- It illustrates the energy loss associated with the magnetization and demagnetization processes.

**10. Applications of magnetic materials:**

- Magnetic materials are used in various devices such as electromagnets, motors, generators, transformers, magnetic resonance imaging (MRI) machines, and electronic compasses.
- Their properties allow for the control and manipulation of magnetic fields for practical purposes.