A simple pendulum of mass 'm', length 'l' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be:
A simple pendulum of mass 'm', length 'l' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be:
Option 1 -
tan⁻¹[ (q * C₂(V₂-V₁)) / (mg * (C₁+C₂)(d-t)) ]
Option 2 -
tan⁻¹[ (q * C₁(V₁+V₂)) / (mg * (C₁+C₂)(d-t)) ]
Option 3 -
tan⁻¹[ (q * C₁(V₁+V₂)) / (mg * (C₁+C₂)(d-t)) ]
Option 4 -
tan⁻¹[ (q * C₂(V₁+V₂)) / (mg * (C₁+C₂)(d-t)) ]
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1 Answer
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Correct Option - 3
Detailed Solution:Tsinθ = qE
Tcosθ = mg
tanθ = qE/mg
E = V/d_eff. V = V? - (-V? ) = V? +V?
C? =kε? A/t, C? =ε? A/ (d-t).
Capacitors are in series. Q=C_eqV. E inside dielectric = σ/ (kε? ) = Q/ (Akε? ).
E in air = σ/ε? = Q/Aε?
Let's follow the solution.
Q = (C? / (C? +C? ) (V? +V? ).
E = E_air = Q/ (Aε? )
tanθ = qQ/ (Aε? mg) = q/ (Aε? mg) * (C? / (C? +C? ) (V? +V? )
Substitute C? and C?
This is getting complicated. The solution directly uses an expression for E. E = Q/C? Aε?
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