Magnetics
13.0 Summary (Important points & formulae)
13.0 Summary (Important points & formulae)
$ \bullet $ Force on a moving charge : The force on a charge $q$ moving with velocity in a magnetic field is given by$${\vec F_m} = qvb\sin \theta $$and the direction of force is given by Fleming left-hand rule. In vector notation, we can write$${\vec F_m} = q\left( {\vec v \times \vec B} \right)$$
$ \bullet $ Lorentz force : When a charged particle moves through a region of space having both $\vec E$ and $\vec B$ field, the net force on the particle called Lorentz force and is given by$$\vec F = \vec Eq + q\left( {\vec v \times \vec B} \right)$$
$ \bullet $ In magnetic field speed and hence kinetic energy of the charged particle remain constant.
$ \bullet $ When charged particle is projected perpendicular to the magnetic field, its path will be circular.
The radius of path$$r = \frac{{mv}}{{qB}}$$The time to complete the circle$$T = \frac{{2\pi m}}{{qB}}$$
$ \bullet $ When charged particle is projected at an angle $θ$ with the magnetic field, its path will be helical. The radius of path
$$r = \frac{{m{v_ \bot }}}{{qB}} = \frac{{mv\sin \theta }}{{qB}}$$and pitch, $$p = \frac{{2\pi mv\cos \theta }}{{qB}}$$
A charged particle $q$ enters normally in a uniform magnetic field. $\vec B$ The magnetic field extends to a distance $x,$ which is less than or equal to the radius of the path, then deviation angle $θ$ is given by$$\sin \theta = \frac{x}{r}$$
$ \bullet $ Hall effect : Hall potential is given by$${V_H} = \frac{{iR}}{{nel}}$$
$ \bullet $ Mass spectrograph : For two isotopes of mass numbers $m_1$ and $m_2$$$\frac{{{m_1}}}{{{m_2}}} = \frac{{{r_1}}}{{{r_2}}}$$
$ \bullet $ Cylotron : If $V$ is the potential and $f$ is the frequency of the $AC$ source used in cylotron, then $K.E.$ of the particle $q$ will be$$K.E=2fqV$$
$ \bullet $ Magnetic force on current carrying conductor :-$$F=Bil\sin \theta$$ and the direction of force can be obtained by Flemings left handrule. In vector notation$${\vec F_m} = i\vec l \times \vec B$$
$ \bullet $ Force on curved conductor :$${\vec F_m} = \int_P^Q {id\vec l} \times \vec B$$
$ \bullet $ Biot Savart Law :- The Biot Savart Law is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current$$dH \propto \frac{{Idl\sin \theta }}{{{x^2}}}$$
