JEE Main:

• Magnitude of electric field due to a point charge

• Shortcut: (E \propto \frac{1}{r^2})
• Trick: Imagine the electric field lines as water flowing out from a point source. The closer you get to the source, the stronger the electric field.

• Magnitude of magnetic field due to a moving charge

• Shortcut: (B \propto \frac{q v \sin \theta}{r})
• Trick: Imagine the magnetic field lines as circles around the moving charge. The stronger the charge and velocity, and the closer you get to the charge, the stronger the magnetic field.

• Force experienced by a moving charge in a magnetic field

• Shortcut: (\overrightarrow{F} = q\overrightarrow{v} \times \overrightarrow{B})
• Trick: Use the right-hand rule to determine the direction of the force.

• Magnetic force on a current-carrying wire

• Shortcut: (F = (\frac{\mu_0}{4 \pi})\frac{2 I_1I_2 l_1 l_2}{d})
• Trick: Imagine two parallel wires carrying current. The closer the wires are, and the stronger the currents, the stronger the magnetic force between them.

• Hall effect: Hall coefficient

• Shortcut: (R_H = \frac{V_h B}{id})
• Trick: The Hall coefficient is a measure of the concentration of charge carriers in a material.

• Cyclotron frequency

• Shortcut: (\omega_c = \frac{qB}{m})
• Trick: The cyclotron frequency is the frequency at which a charged particle orbits in a magnetic field.

• Magnetic moment of a current loop

• Shortcut: (\overrightarrow{M} = I\overrightarrow{A})
• Trick: The magnetic moment of a current loop is a measure of its strength as a magnet.

• Torque experienced by a current loop in a magnetic field

• Shortcut: (\overrightarrow{\tau} = \overrightarrow{M} \times \overrightarrow{B} = NI\overrightarrow{A} \times \overrightarrow{B})
• Trick: The torque on a current loop in a magnetic field is a measure of the force that the magnetic field exerts on the loop.

CBSE Board:

• Electric field due to a point charge

• Shortcut: (E \propto \frac{1}{r^2})
• Trick: Imagine the electric field lines as water flowing out from a point source. The closer you get to the source, the stronger the electric field.

• Magnetic field due to a current-carrying wire

• Shortcut: (B \propto \frac{I}{d})
• Trick: Imagine the magnetic field lines as circles around the wire. The stronger the current and the closer you get to the wire, the stronger the magnetic field.

• Force experienced by a moving charge in a magnetic field

• Shortcut: (\overrightarrow{F} = q\overrightarrow{v} \times \overrightarrow{B})
• Trick: Use the right-hand rule to determine the direction of the force.

• Magnetic force on a current-carrying wire

• Shortcut: (F = (\frac{\mu_0}{4 \pi})\frac{2 I_1I_2 l_1 l_2}{d})
• Trick: Imagine two parallel wires carrying current. The closer the wires are, and the stronger the currents, the stronger the magnetic force between them.

• Cyclotron frequency

• Shortcut: (\omega_c = \frac{qB}{m})
• Trick: The cyclotron frequency is the frequency at which a charged particle orbits in a magnetic field.

• Magnetic moment of a current loop

• Shortcut: (\overrightarrow{M} = I\overrightarrow{A})
• Trick: The magnetic moment of a current loop is a measure of its strength as a magnet.

• Torque experienced by a current loop in a magnetic field

• Shortcut: (\overrightarrow{\tau} = \overrightarrow{M} \times \overrightarrow{B} = NI\overrightarrow{A} \times \overrightarrow{B})
• Trick: The torque on a current loop in a magnetic field is a measure of the force that the magnetic field exerts on the loop.

• Magnetic resonance imaging (MRI)

• Shortcut: MRI uses a strong magnetic field and radio waves to create images of the inside of the body.

• Mass spectrometer

• Shortcut: A mass spectrometer uses a magnetic field to separate charged particles based on their mass-to-charge ratio.

• Cyclotron

• Shortcut: A cyclotron is a type of particle accelerator that uses a strong magnetic field to accelerate charged particles.

• Synchrotron

• Shortcut: A synchrotron is a type of particle accelerator that uses a strong magnetic field to keep charged particles in a circular path.