04Class 12 Physics

Moving Charges and Magnetism formulas

Magnetic force, Biot-Savart and Ampere's law formulas for Moving Charges and Magnetism. Use the right-hand rule on every question.

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Force

Lorentz force: $\displaystyle \vec F = q(\vec E + \vec v\times\vec B)$
Force on a wire: $\displaystyle \vec F = I\vec L\times\vec B$
Radius in a magnetic field: $\displaystyle r = \frac{mv}{qB}$
Cyclotron frequency: $\displaystyle \nu = \frac{qB}{2\pi m}$
It doesn't depend on speed.
Force between parallel wires: $\displaystyle \frac{F}{L} = \frac{\mu_0 I_1I_2}{2\pi d}$
Like currents attract.

Biot-Savart law: $\displaystyle d\vec B = \frac{\mu_0}{4\pi}\frac{I\,d\vec l\times\hat r}{r^2}$
Long straight wire: $\displaystyle B = \frac{\mu_0 I}{2\pi r}$
Centre of a circular loop: $\displaystyle B = \frac{\mu_0 I}{2R}$
Axis of a circular loop: $\displaystyle B = \frac{\mu_0 IR^2}{2(R^2 + x^2)^{3/2}}$
Ampere's law: $\displaystyle \oint\vec B\cdot d\vec l = \mu_0 I_{\text{enclosed}}$
Long solenoid: $\displaystyle B = \mu_0 nI$
n is turns per unit length.

Magnetic moment: $\displaystyle \vec m = NI\vec A$
Torque on a loop: $\displaystyle \vec\tau = \vec m\times\vec B$
Galvanometer to ammeter: $\displaystyle S = \frac{I_gG}{I - I_g}$
Shunt in parallel.
Galvanometer to voltmeter: $\displaystyle R = \frac{V}{I_g} - G$
High resistance in series.

Expecting a magnetic force to change a particle's speed. It's always perpendicular to v, so it does no work.
Forgetting the charge's sign. For a negative charge, the force is opposite to what the right-hand rule gives.
Using the infinite-wire result on a short segment.

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