Motion of Charged Particle in Magnetic Field (Lorentz Force Law) :
`text(Force on moving charge :)`
The magnetic force on a charge q, moving with velocity `v` in a magnetic field `B` is given by
`vecF = q(vecv xx vecB)`
This is known as the Lorentz force law. If electric and magnetic both fields are present the net force on q would be `vecF = q[vecE + (vecv xx vecB)]`
`text(Magnitude of magnetic force :)`
`F = qvBsintheta` (where q is without sign and `theta` is the angle between `vecv & vecB`.
`text(Direction :)`
Force is perpendicular to both velocity and magnetic field. Its direction is same as `vecv xx vecB` if q is positive and opposite of `vecv xx vecB` if `q` is negative.
Cases:
(i) If `q = 0`, then `F = 0` i.e., neutral particles do not experience magnetic force.
(ii) If `v = 0` , then `F = 0` i.e., stationary charges do not experience magnetic force.
(iii) If `theta = 0` or `pi` , then `F = 0` i.e., when a charge moves parallel or anti-parallel to magnetic field it does not experience magnetic force.
(iv) If a = `(pi)/2` then `F = qvB` is maximum. If `B` is uniform the particle will trace a circular path, if `r` is the radius of the path then for circular motion.
`(mv^2)/r = qvB`
=> `r = (mv)/(qB) = p/(qB) = sqrt(2mE)/(qB)`
`text(Time period of circular motion :)`
`T = (2pi)/v`
=> `T = (2pim)/(qB)`
The magnetic force on a charge q, moving with velocity `v` in a magnetic field `B` is given by
`vecF = q(vecv xx vecB)`
This is known as the Lorentz force law. If electric and magnetic both fields are present the net force on q would be `vecF = q[vecE + (vecv xx vecB)]`
`text(Magnitude of magnetic force :)`
`F = qvBsintheta` (where q is without sign and `theta` is the angle between `vecv & vecB`.
`text(Direction :)`
Force is perpendicular to both velocity and magnetic field. Its direction is same as `vecv xx vecB` if q is positive and opposite of `vecv xx vecB` if `q` is negative.
Cases:
(i) If `q = 0`, then `F = 0` i.e., neutral particles do not experience magnetic force.
(ii) If `v = 0` , then `F = 0` i.e., stationary charges do not experience magnetic force.
(iii) If `theta = 0` or `pi` , then `F = 0` i.e., when a charge moves parallel or anti-parallel to magnetic field it does not experience magnetic force.
(iv) If a = `(pi)/2` then `F = qvB` is maximum. If `B` is uniform the particle will trace a circular path, if `r` is the radius of the path then for circular motion.
`(mv^2)/r = qvB`
=> `r = (mv)/(qB) = p/(qB) = sqrt(2mE)/(qB)`
`text(Time period of circular motion :)`
`T = (2pi)/v`
=> `T = (2pim)/(qB)`
