Physics

Problem

Two particles

A

and

B

, each carrying charge magnitude

q

, move through the same region of uniform magnetic field

\mathbf B

. Particle

A

has speed

v_{A}

at an angle

\theta_{A}

\mathbf B

; particle

B

has speed

v_{B}

at an angle

\theta_{B}

\mathbf B

. a. (i) Starting from the expression for magnetic force on a moving charge, show that the ratio of the magnitudes of the forces on

A

and

B

\dfrac{F_{A}}{F_{B}}=\dfrac{v_{A}\sin\theta_{A}}{v_{B}\sin\theta_{B}}

. b. (ii) Given

v_{A}=4.0\times10^{5}\,\text{m s}^{-1}

v_{B}=3.0\times10^{5}\,\text{m s}^{-1}

\theta_{A}=60^{\circ}

and

\theta_{B}=45^{\circ}

, calculate

F_{A}/F_{B}

. c. (iii) If the masses of the particles are

m_{A}=2m_{B}

, compare the magnitudes of their initial accelerations in the magnetic field.