Work done by the electric force in a moving charge:

$\overline{){\mathbf{W}}{\mathbf{=}}{\mathbf{-}}{\mathbf{q}}{\mathbf{\u2206}}{\mathbf{V}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

Centripetal force:

$\overline{){{\mathbf{F}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{{\mathbf{mv}}^{\mathbf{2}}}{\mathbf{r}}}$

Magnetic force on moving charge:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{q}}{\mathbf{v}}{\mathbf{B}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\theta}}}$

The kinetic energy of the ions is equal to the work done by the electric force.

|W| = |K|

qΔV = (1/2)mv^{2}

v = (2qΔV/m)^{(1/2)}

The net force on the ions is due to the magnetic force.

Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?

A) 2/⎷2

B) R/2

C) 3R

D) ⎷2R

E) 4R

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Circular Motion of Charges in Magnetic Fields concept. You can view video lessons to learn Circular Motion of Charges in Magnetic Fields. Or if you need more Circular Motion of Charges in Magnetic Fields practice, you can also practice Circular Motion of Charges in Magnetic Fields practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Pantea's class at University of Windsor.