# After being accelerated to a speed of 1.05\times105 m/s , the particle enters a uniform magnetic...

## Question:

After being accelerated to a speed of 1.05 {eq}\times {/eq}105 m/s , the particle enters a uniform magnetic field of strength 0.900 T and travels in a circle of radius 34.0 cm (determined by observing where it hits the screen as shown in the figure). The results of this experiment allow one to find m/q. Find the ratio m/q for this particle. Express your answer numerically in kilograms per coulomb.

## Magnetic Lorentz force

From the equation of Magnetic Lorentz force we know that the force on the given section of wire is given by the cross product of the current and the magnetic field. That means if the current and the magnetic field is in same direction then the magnetic force would be zero.

Given

The velocity of the particle {eq}\displaystyle V = 1.05*10^{5} \ m/s {/eq}

Magnetic field (B) = 0.9 T

Radius of the circle (R) = 0.34 m

Now we know that when particle enters into the magnetic field, then

{eq}\displaystyle F = \dfrac{mV^{2}}{R} \\ qVB = \dfrac{mV^{2}}{R} \\ \dfrac{m}{q} = \dfrac{RB}{V} \\ \dfrac{m}{q} = \dfrac{0.34*0.9}{1.05*10^{5}} \\| \dfrac{m}{q} = 2.914*10^{-6} {/eq} 