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Need help in understanding the direction of magnetic force in the magnetic field!Totally confused by directions.

Why is it that magnetic force is perpendicular to the direction of magnetic field and velocity of charged particle. Why is it(force) not in the same direction as the magnetuc field

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A magnetic field exerts a force on a moving charge. Given a magnetic field, $\vec{B}$, and a charge, $q$, moving with velocity, $\vec{v}$, the magnetic force, $\vec{F}$, on the charge is:$$\vec{F}= q(\vec{v} \times \vec{B})$$

The directions of these with respect to one another can be found using the right hand rule. See the picture below.

enter image description here

The magnetic force is perpendicular to the direction of magnetic field because $\vec{v}$ and $\vec{B}$ are in cross product. Give this a read.

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A more comprehensive and deeper explanation of the Lorentz-force is based on relativistic electrodynamics as given in:

http://chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf

by Hans De Vries.

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