Question

If a charged particle goes unaccelerated in a region containing electric and magnetic fields,

• A. $\overrightarrow{E}$ must be perpendicular to $\overrightarrow{B}$
• B. $\overrightarrow{v}$ must be perpendicular to $\overrightarrow{E}$
• C. $\overrightarrow{v}$ must be perpendicular to $\overrightarrow{B}$
• D. $E$ must be equal to $vB$

Answer 1

Answer: (A), (B)

The correct options are
A $\overrightarrow{E}$ must be perpendicular to $\overrightarrow{B}$
B $\overrightarrow{v}$ must be perpendicular to $\overrightarrow{E}$

If a charged particle goes unaccelerated in a region containing electric and magnetic fields
$\left|q\overrightarrow{E}\right|=|q\overrightarrow{v}\times \overrightarrow{B}|\Rightarrow \left|\overrightarrow{E}\right|=|\overrightarrow{v}\times \overrightarrow{B}|\Rightarrow E=vB\sin \theta$

If the acceleration and in turn the velocity of the charged particle remains constant in a region containing electric and magnetic fields, then electric fieldis perpendicular to both velocity and magnetic field.