Answer:
1.8 cm
Explanation:
[tex]m[/tex] = mass of the singly charged positive ion = 3.46 x 10⁻²⁶ kg
[tex]q[/tex] = charge on the singly charged positive ion = 1.6 x 10⁻¹⁹ C
[tex]\Delta V[/tex] =Potential difference through which the ion is accelerated = 215 V
[tex]v[/tex] = Speed of the ion
Using conservation of energy
Kinetic energy gained by ion = Electric potential energy lost
[tex](0.5) m v^{2} = q \Delta V\\(0.5) (3.46\times10^{-26}) v^{2} = (1.6\times10^{-19}) (215)\\(1.73\times10^{-26}) v^{2} = 344\times10^{-19}\\v = 4.5\times10^{4} ms^{-1}[/tex]
[tex]r[/tex] = Radius of the path followed by ion
[tex]B[/tex] = Magnitude of magnetic field = 0.522 T
the magnetic force on the ion provides the necessary centripetal force, hence
[tex]qvB = \frac{mv^{2} }{r} \\qB = \frac{mv}{r}\\r =\frac{mv}{qB}\\r =\frac{(3.46\times10^{-26})(4.5\times10^{4})}{(1.6\times10^{-19})(0.522)}\\r = 0.018 m \\r = 1.8 cm[/tex]
