IB Physics SL D.3 Motion in electromagnetic fields questions

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Question 1

Multiple choiceMedium1 mark

Particles X and Y, each with charge magnitude $q$ enter the same uniform magnetic field at right angles to the field with equal speeds. Only magnetic forces act. Each follows a semicircular path, and Y’s path radius is twice X’s. Which row gives the ratios $(|q|/m)_Y/(|q|/m)_X$ and $K_Y/K_X$ respectively, after both particles complete their semicircles?

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Answer: B. The magnetic force supplies the centripetal force, so $|q|vB=mv^2/r$ giving $|q|/m=v/(Br)$ With equal speeds and the same field, the charge-to-mass ratio is inversely proportional to radius, so the ratio for Y and X is $1/2$ Equal charge magnitudes then give $m_Y/m_X=2$ and equal speeds give $K_Y/K_X=2$ The magnetic force is perpendicular to the motion, so neither particle’s kinetic energy changes during its semicircle.

A: Gets the charge-to-mass ratio right but assumes equal speeds mean equal kinetic energies, overlooking the different masses.
C: Treats charge-to-mass ratio as directly proportional to radius; this also gives the inverse mass and kinetic-energy ratio.
D: Reverses the charge-to-mass ratio’s dependence on radius but correctly uses $K\propto m$ at equal speed.
Remember: a magnetic force changes a particle’s direction, not its kinetic energy.

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