A rod of mass m (uniformly distributed) and length ℓ is hinged about point O in a uniform vertical electric field as shown. Linear charge density of rod varies with x as λ = λ 0 x . Electric field f

Question

A rod of mass m (uniformly distributed) and length ℓ is hinged about point O in a uniform vertical electric field as shown. Linear charge density of rod varies with x as λ = λ 0 ​ x . Electric field for which rod remain horizontal is 2 λ 0 ​ ℓ 2 nmg ​ . Find value of n.

TestHub · Accepted Answer

For rotational equilibrium torque of electric field should be equal and opposite to torque of weight Torque on small element dq.

$d τ = Edq x τ = \int_{L} Exdq τ = \int_{0}^{C} Ex \cdot λ_{0} xdx & Put τ = mg (\frac{L}{2})$

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