Question

Association of mass with charge​

Answer 1

Answer: The charge-to-mass ratio (Q/m) of an object is, as its name implies, the charge of an object divided by the mass of the same object. This quantity is generally useful only for objects that may be treated as particles. For extended objects, total charge, charge density, total mass, and mass density are often more useful.

Derivation:

{\displaystyle qvB=mv{\frac {v}{r}}} {\displaystyle qvB=mv{\frac {v}{r}}} or {\displaystyle {\frac {q}{m}}={\frac {v}{Br}}} {\displaystyle {\frac {q}{m}}={\frac {v}{Br}}} (1)

Since {\displaystyle F_{electric}=F_{magnetic}} {\displaystyle F_{electric}=F_{magnetic}},

{\displaystyle Eq=Bqv} {\displaystyle Eq=Bqv} or {\displaystyle v={\frac {E}{B}}} {\displaystyle v={\frac {E}{B}}} (2)

Equations (1) and (2) yield

{\displaystyle {\frac {q}{m}}={\frac {E}{B^{2}r}}} {\displaystyle {\frac {q}{m}}={\frac {E}{B^{2}r}}}

Explanation: