Verified Solution • 2025–26 Session moderate

QJEEM21Ph4b0b: JEE Main 2021 Physics - Class 12 JEEM21Ph4b0b Solution: A simple pendulum of mass 'm', length 'l' and charge '+ q'…

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

JEE Main 2021 (Online) 27th July Evening Shift Physics - Capacitor Question 77 English

Multiple Choice Options

  • A tan⁡−1[qmg×C1(V2−V1)(C1+C2)(d−t)]{\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_1}({V_2} - {V_1})} \over {({C_1} + {C_2})(d - t)}}} \right]
  • B tan⁡−1[qmg×C2(V2−V1)(C1+C2)(d−t)]{\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_2}({V_2} - {V_1})} \over {({C_1} + {C_2})(d - t)}}} \right]
  • C tan⁡−1[qmg×C2(V1+V2)(C1+C2)(d−t)]{\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_2}({V_1} + {V_2})} \over {({C_1} + {C_2})(d - t)}}} \right]
  • D tan⁡−1[qmg×C1(V1+V2)(C1+C2)(d−t)]{\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_1}({V_1} + {V_2})} \over {({C_1} + {C_2})(d - t)}}} \right]

Step-by-Step Verified Solution

JEE Main 2021 (Online) 27th July Evening Shift Physics - Capacitor Question 77 English Explanation 1
Let E be electric field in air

T sin θ\theta = qE

T cos θ\theta = mg

tan θ\theta = qEmg{{qE} \over {mg}}

JEE Main 2021 (Online) 27th July Evening Shift Physics - Capacitor Question 77 English Explanation 2
Q=[C1C2C1+C2][V1+V2]Q = \left[ {{{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right][{V_1} + {V_2}]

E=QA∈0=[C1C2C1+C2][V1+V2]A∈0E = {Q \over {A{ \in _0}}} = \left[ {{{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right]{{[{V_1} + {V_2}]} \over {A{ \in _0}}}

C1=∈0Ad−t⇒E=C2[V1+V2](C1+C2)(d−t){C_1} = {{{ \in _0}A} \over {d - t}} \Rightarrow E = {{{C_2}[{V_1} + {V_2}]} \over {({C_1} + {C_2})(d - t)}}

Now, θ=tan⁡−1[q.Emg]\theta = {\tan ^{ - 1}}\left[ {{{q.E} \over {mg}}} \right]

θ=tan⁡−1[qmg×C2(V1+V2)(C1+C2)(d−t)]\theta = {\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_2}({V_1} + {V_2})} \over {({C_1} + {C_2})(d - t)}}} \right]

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