Force Acting on Moving Charges: Practice Problem & Solution
If a charged particle goes unaccelerated in a region containing electric & magnetic fields: (a) \(\vec{E}\) must be perpendicular to \(\vec{B}\) (b) \(\vec{v}\) must be perpendicular to \(\vec{E}\) (c) \(\vec{v}\) must be perpendicular to \(\vec{B}\) (d) \(E\) must be equal to \(vB\)
Solution Explained:
To solve this problem, we apply the core principles of Force Acting on Moving Charges. Understanding the underlying formula is key to arriving at the correct answer below:
For the net force to be zero, \(\vec{F}_e + \vec{F}_b = 0 ⇒ \vec{E} = -(\vec{v} \times \vec{B})\). Since \(\vec{E}\) is the cross product, it must be perpendicular to both \(\vec{B}\) and \(\vec{v}\).
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