Maximum kinetic energy of the positive ion in the cyclotron is

Options

A. `(q^(2)Br_(0))/(2m)`
B. `(qB^(2)r_(0))/(2m)`
C. `(q^(2)B^(2)r_(0)^(2))/(2m)`
D. `(qBr_(0))/(2m^(2))`

Answer

C

Explanation

`k_(max)=(1)/(2)mv^(2)` and `r_(0)=(mv)/(qB)impliesv=(qBr_(0))/(m)`
` impliesk_(max)=(1)/(2)m((qBr_(0))/(m))^(2)=(q^(2)B^(2)r_(0)^(2))/(2m)`