An electrometer consists of a fixed vertical metal bar OB at the top of which is attached a thin rod OA which gets deflected from the bar under the action of an electric charge (fig.). The rod can rotate in vertical plane about fixed horizontal axis passing through O. The reading is taken on a quadrant graduated in degrees. The length of the rod is λ and its mass is m. What will be the charge when the rod of such an electrometer is deflected through an angle α in equilibrium. Find the answer using the following two assumptions:
The charge on the electrometer is equally distributed between the bar & the rod and the charges are concentrated at point A on the rod & at point B on the bar.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
q = 4 λ 
sin 
Sol. The electrostatic force exerted by charge at B on charge at A is
F e = 
= 
= 
The rod AO is in equilibrium, hence net torque on rod about point O is
F e λ sin 
– mg (sin α) 
= 0
⇒ solving, we get
q = 4 λ 
sin 
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