Question

Magnetic force acting on the charged particle projected perpendicular to the magnetic field is perpendicular to ${{V}^{n}}$ . Where V is the speed, Find n

Answer 1

The space around the poles of a magnet is called the magnetic field, and is represented by magnetic lines of force. The force exerted on one magnet by another one, either of attraction or of repulsion is called the magnetic field. According to coulomb's first law unlike poles attract each other and like poles repel each other

Complete step-by-step solution:
The magnetic force is caused by the motion of charges and it is the basic force responsible for attraction and repulsion.
The magnitude of magnetic force is given by:
$F=qBV$
Where q= charge
B =magnetic field
V=velocity
Magnetic force acting on the charged particle projected perpendicular to magnetic field is perpendicular to ${{V}^{n}}$ is given by:
$F=\dfrac{m{{V}^{2}}}{r}$ $\cdots \cdots (1)$
Where $r=\dfrac{mV}{qB}$
After substituting this in equation (1)
We get $F=\dfrac{m{{V}^{2}}}{\dfrac{mV}{qB}}$
$\begin{aligned} & F=qBV \\\ & F\propto {{V}^{1}} \\\ \end{aligned}$
We know that $V=\dfrac{qBr}{m}$
After substituting this in equation (1) $F=\dfrac{m{{v}^{2}}}{r}$
$F=\dfrac{{{q}^{2}}{{B}^{2}}r}{m}$
$F\propto r$
Therefore ${{r}^{n}}={{r}^{1}}$
The value of n=1.

Note: Students magnetic lines of force which originate from a north pole and end at south pole and there cannot exist an isolated north pole or south pole. Magnetic monopoles do not exist in nature. Earth which produces its own magnetic field. Tesla is a unit of magnetic field strength (magnetic flux density).