MHT CET · Physics · Magnetic Effects of Current
Two particles of masses \(m_{a}\) and \(m_{b}\) and same charge are projected in a perpendicular magnetic field. They travel along circular paths of radius \(r_{a}\) and \(r_{b}\) such that \(r_{a}>r_{b}\). Then which is true?
- A \(m_{a} v_{a}>m_{b} v_{b}\)
- B \(m_{a}>m_{b}\) and \(v_{a}>v_{b}\)
- C \(m_{a}=m_{b}\) and \(v_{a}>v_{b}\)
- D \(m_{b} v_{b}>m_{a} v_{a}\)
Answer & Solution
Correct Answer
(A) \(m_{a} v_{a}>m_{b} v_{b}\)
Step-by-step Solution
Detailed explanation
Radius of circular path \(r_{a}=\frac{m_{a} v_{a}}{q B}\)
and
\(
r_{b}=\frac{m_{b} v_{b}}{q B}
\)
According to question
\(
r_{a}>r_{b}
\)
\(\therefore\)
\(
\frac{m_{a} v_{a}}{q B}>\frac{m_{b} v_{b}}{q B}
\)
or \(\quad m_{a} v_{a}>m_{b} v_{b}\)
and
\(
r_{b}=\frac{m_{b} v_{b}}{q B}
\)
According to question
\(
r_{a}>r_{b}
\)
\(\therefore\)
\(
\frac{m_{a} v_{a}}{q B}>\frac{m_{b} v_{b}}{q B}
\)
or \(\quad m_{a} v_{a}>m_{b} v_{b}\)
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