In the figure, a particle moves along a circle in a region of uniform magnetic f

Question

In the figure, a particle moves along a circle in a region of uniform magnetic field with magnitude B. The particle is either a proton or an electron (you must decide which based on the figure). It experiences a magnetic force of magnitude F. What are (a) the particle's speed, (b) the radius of the circle, and (c) the period of the motion? The charge of an electron is -e and its mass is m_e. The charge of a proton is e and its mass is m_p. State your answers in terms of the given variables. (a) v = F/(e middot B) (b) r = (m) middot F/((e x B))^2 (c) T = 2 pi (m) middot/e x B

Explanation / Answer

F = q (v x B)

for given position,

F = i^

v -> -j

B -> k

v x B = -j x k = -i

hence q is negative so particle is electron.

(A) F = q v B

v = F / (e B)

(b) F = m v^2 / r = me (F^2 / e^2 B^2) / r

r = me F / e^2 B^2

(c) T = 2 pi r / v = 2pi (me F / e^2 B^2) / ( F / e B)

T = 2 pi me / e B

(don't use dot or cross that is just multiplication because we have to find only magnitude)

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