Question

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A pendulum bob of mass m carrying a charge q is at rest in a uniform horizontal electric field of intensity E. The tension in the thread is

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Answer 1

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GIVEN :-

• A pendulum Bob of mass ‘m’ carrying a charge ‘q’ is at rest in an uniform horizontal electric field of intensity ‘E’ .

• Mass = m
• charge = q
• Electric field intensity = E

CONCEPT :-

✴️ A charge is placed in an uniform horizontal electric field, so obviously a force is generate on the charge particle and small displacement is occurring in the bob of the pendulum[where charge is present] .

✴️ And The bob of the pendulum is making an angle ‘θ’ with the thread .

To Find :-

• The Tension in the thread .

CALCULATION:-

☞ See the attachment picture for Free body diagram .

✪ Let, ‘T’ be the tension in the thread.

▼ So, In Equilibrium

$\checkmark\:\rm{\underline{mg\:=\:T\cos{\theta}\:}}$

$\bigstar\:\rm{\boxed{\purple{T\:=\:\dfrac{mg}{\cos{\theta}}\:}}}$

✪ And

$\checkmark\:\rm{\underline{qE\:=\:T\sin{\theta}\:}}$

$\bigstar\:\rm{\boxed{\blue{T\:=\:\dfrac{qE}{\sin{\theta}}\:}}}$