A charged particle is observed traveling in a circular path of radius R in a uniform magnetic field. If the particle were traveling twice as fast, the radius of the circular path would be
A) $8 R$.
B) $R / 2$.
C) $4 R$.
D) $R / 4$.
E) $2 R$.

Question

A charged particle is observed traveling in a circular path of radius R in a uniform magnetic field. If the particle were traveling twice as fast, the radius of the circular path would be 
A) $8 R$.
B) $R / 2$.
C) $4 R$.
D) $R / 4$.
E) $2 R$.

Quizplus · Accepted Answer

The radius of the circular path $r$ for a charged particle moving in a magnetic field is given by $r = \frac{mv}{qB}$, where $m$ is the mass of the particle, $v$ is its velocity, $q$ is its charge, and $B$ is the magnetic field strength. Doubling the velocity ($v \rightarrow 2v$) would double the radius ($r \rightarrow 2r$), making the correct answer $2 R$.

A Charged Particle Is Observed Traveling in a Circular Path 8R8 R8R

A Charged Particle Is Observed Traveling in a Circular Path $8 R$