If q is the electric charge,B is the magnetic | vedclass

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(D) In a cyclotron,the radius $R$ of the path of an ion is given by the relation $R = \frac{mv}{qB}$,where $v$ is the velocity of the ion.Rearranging

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$\frac{q^2B^2R^2}{2m}$

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(D) In a cyclotron,the radius $R$ of the path of an ion is given by the relation $R = \frac{mv}{qB}$,where $v$ is the velocity of the ion.Rearranging this for velocity,we get $v = \frac{qBR}{m}$.The kinetic energy $(K.E.)$ of the ion is given by the formula $K.E. = \frac{1}{2}mv^2$.Substituting the expression for $v$ into the kinetic energy formula:$K.E. = \frac{1}{2}m \left( \frac{qBR}{m} \right)^2$$K.E. = \frac{1}{2}m \left( \frac{q^2B^2R^2}{m^2} \right)$$K.E. = \frac{q^2B^2R^2}{2m}$.

If $q$ is the electric charge,$B$ is the magnetic field,$R$ is the dee radius,and $m$ is the mass of ions,the kinetic energy of the ions in a cyclotron is given by

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