Foolish \(\alpha \) Particle in Variable Magnetic Field

Electricity and Magnetism Level 5

Let a variable magnetic field exist in \(XYZ\) plane only in 1st quadrant, such that its magnitude is varying with distance \(x\) \((B={ B }_{ 0 }x)\) and direction in positive \(Z\)-axis.

Now an \(\alpha\)-particle of mass \(m\) and charge \(q\) enters in this magnetic field at origin with velocity \({V}_{0}\) and direction in positive \(X\)-axis.

Then find the radius of curvature of trajectory of particle at the instant when the particle displaced maximum distance in \(X\)-direction

Details and assumptions

1)\({ B }_{ 0 }=1.67\times { 10 }^{ -27 }T\)

2)\({ V }_{ 0 }=1.28\times { 10 }^{ -18 }m/s\)

3)\({ m }_{ \alpha }=6.68\times { 10 }^{ -27 }Kg\)

4)\({ q }_{ \alpha }=3.2\times { 10 }^{ -19 } C\)

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