A proton (of mass kg) and an electron (of mass kg) both travelling at ms-1 enter a…

PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism

Problem

A proton (of mass

1.67 \times 10^{-27}

kg) and an electron (of mass

9.1 \times 10^{-31}

kg) both travelling at

5.0 \times 10^6

ms^-1 enter a magnetic field at right angles to the field's direction. The proton and the electron have opposite charges of

+1.6 \times 10^{-19}

C and

-1.6 \times 10^{-19}

C, respectively. The magnetic field has a magnetic flux density of 4 mT. (a) Calculate the size of the magnetic force on (i) the proton. (ii) the electron. (b) Hence, calculate the radius of the circular path in the magnetic field that will be followed by (i) the proton. (ii) the electron. (c) Determine the time it takes to make one complete circle for (i) the proton. (ii) the electron. (d) In another example, using the same magnetic field as previously, the electron and the proton now enter the magnetic field with a velocity of

1.0 \times 10^7

ms^-1 (i.e. double their previous velocities). (i) How will the new magnetic force on each particle differ from previously? (ii) How will the new radii of the two paths differ from previously? (iii) How will the time to make one complete circle for each of the particles differ from before? (iv) Derive an expression for the time taken for one complete circle in terms of

B

q

and

m

. (v) What do you notice about the relationship between

v

and the time to complete a circle?

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