Physics

Problem

A proton enters a region of uniform magnetic field of magnitude

0.30\,\text{T}

with a speed of

2.0\times10^{7}\,\text{m s}^{-1}

, making an angle of

45^{\circ}

with the field. a. (i) Calculate the magnitude of the initial magnetic force on the proton. b. (ii) If the magnetic field is increased to

0.36\,\text{T}

while the speed and direction remain the same, determine the percentage change in the magnitude of the force.

Intuitive explanation

The key is to decompose the proton's velocity into components parallel and perpendicular to the magnetic field. The parallel component passes through unchanged, while the perpendicular component experiences a magnetic force that curves the proton into a circular path. Together, these create a helical trajectory—the proton spirals along the field direction while circling around it. Focus on finding the radius of that circular motion and the period of one complete loop.

Intuitive explanation

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