Physics

Problem

A proton of charge

+e

enters a uniform magnetic field of magnitude

0.50\,\text{T}

with speed

2.0\times10^{6}\,\text{m\,s}^{-1}

. The angle between

\vec v

and

\vec B

is slowly reduced from

90^{\circ}

0^{\circ}

while keeping the speed and the field magnitude constant. a. (a) Derive an expression for the magnitude of the magnetic force on the proton as a function of the angle

\theta

between

\vec v

and

\vec B

. b. (b) Calculate the magnetic force when

\theta=30^{\circ}

60^{\circ}

and

90^{\circ}

. c. (c) At what angle

\theta

will the magnetic force on the proton be

3.0\times10^{-13}\,\text{N}

? Show all working steps. d. (d) Explain physically why the magnetic force vanishes when

\theta

approaches

0^{\circ}

even though both

v

and

B

are non-zero.

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