Physics Problems & Solutions: Electromagnetism - Electric and Magnetic Forces

A charge particle is released from rest in a region where there is a constant electric field and a constant magnetic field. If the two fields are parallel to each other, the path of the particle is a

A. circle
B. parabola
C. helix
D. cycloid
E. straight line

(GR8677 #25)

Solution:

$\vec{F}= \vec{F}_E+\vec{F}_B = q(\vec{E}+\vec{v}\times \vec{B})$

Electric Force: $\vec{F}_E = q\vec{E}$
→ the path of the particle is parallel to the electric field.
→ the velocity of particle has the same direction with the electric field.

Magnetic Force/Lorentz Force: $\vec{F}_B = q(\vec{v}\times \vec{B})$

If $\vec{E} \parallel \vec{B}\rightarrow \vec{v} \parallel \vec{B}\rightarrow \vec{v} \times \vec{B}= 0$
→ no magnetic field contribution
→ the path of the particle is a straight line, parallel to the electric field.

Answer: E

Electromagnetism - Electric and Magnetic Forces

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