A current carrying is placed vertically and a particle of mass m with charge Q is released from rest

Question

A current carrying is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid. If g is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy:

Accepted Answer

Since the solenoid is placed vertically, the magnetic field inside the solenoid will be either along - y or +y axis.

⇒ Particle will gain velocity along -y axis.

$${\Rightarrow \ {\overrightarrow{F}}_{B} = q(\overrightarrow{v} \times \overrightarrow{B}) }{\Rightarrow \ {\overrightarrow{F}}_{B} = 0 }{\Rightarrow \ {\overrightarrow{F}}_{\text{net~}} = mg }{\Rightarrow \ a_{\text{net~}} = g }$$

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