Question

A SO4 2- ion is accelerated by 1000 volts pass through a velocity selector and make a semi circle of 2.4cm in the deflection area. Find

a)the magnetic field in the deflection and velocity selector area
b)the electric field in the velocity selector area

Answer 1

TOP QUESTION... the answers are below

Answer 2

Oooh, accelerator physics.

To get the magnetic field, start from equating Lorentz force to centripetal force:
\[ \vec{F} = q\vec{v}\times\vec{B} = (-\hat{\vec{r}})\frac{mv^2}{r}\]
Since you don't care about direction
\[qvB = \frac{mv^2}{r}\]
which easily reduces to
\[qB = \frac{mv}{r}\]
the ions have two extra electrons, so
\[q = 2e = 2 \times 1.6 \times 10^{-19}\text{ C}\]
You can get the kinetic energy from multiplying charge and voltage.
\[qV = \frac12mv^2\]
You can get mass from the mass numbers of Sulphur (32) and Oxygen (16) and the nucleon mass
\[m_{p / n} = 1.67\times10^{-27}\text{ kg} \approx 1\text{ GeV c}^{-2}\]

That's all you need to know for magnetic field.

For electric field you must equate the force from the electric field with Lorentz force, since the electric field kept the particle in a straight line
\[ F = qvB = qE\]
\[E = vB\]