MHT CET · Physics · Magnetic Effects of Current
An electron at rest is accelerated by a potential ' \(\mathrm{V}_{1}\) ', in uniform magnetic field
experiences a force 'F \(1^{\prime}\). When potential is changed to \({ }^{\prime} \mathrm{V}_{2}^{\prime}\) ', the force experienced
by the electron gets doubled. The ratio of \(V_{1}\) to \(V_{2}\) is
- A \(4: 1\)
- B \(2: 1\)
- C \(1: 2\)
- D \(1: 4\)
Answer & Solution
Correct Answer
(D) \(1: 4\)
Step-by-step Solution
Detailed explanation
An electron at rest is accelerated by a potential ' \(V_{1}\) ', in uniform field experiences a force ' \(F_{1}\) '. When potential is changed to ' \(V_{2}\) ', the force experienced by the electron gets doubled. The ratio of \(V_{1}\) to \(V_{2}\) is \(1: 2\).
\(\mathrm{F}_{1}=\frac{\mathrm{eV}_{1}}{\mathrm{~d}} 2 \mathrm{F}_{1}=\frac{\mathrm{eV}_{2}}{\mathrm{~d}}\)
\(\frac{V_{1}}{V_{2}}=\frac{1}{2}\)
\(\mathrm{F}_{1}=\frac{\mathrm{eV}_{1}}{\mathrm{~d}} 2 \mathrm{F}_{1}=\frac{\mathrm{eV}_{2}}{\mathrm{~d}}\)
\(\frac{V_{1}}{V_{2}}=\frac{1}{2}\)
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