Difficult Conceptual Numericals

## Electric Charges And Fields

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Find the electric flux crossing the wire frame ABCD of length l, width b, and center at a distance OP=d from an infinite line of charge with linear charge density . Consider that the plane of the frame is perpendicular to the line OP Fig.
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Four point charges of charge are placed on the vertices of square and body of mass m and charge q is placed perpendicular to the centre of sqaure at a distance from the centre. Take the distance between centre and vertices of the sqaure to be . What should be the value of Q in order that this body may be in equilibrium?
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A bob of a simple pendulum of mass gm with a positive charge is oscillating with a time period .An electric field of intensity  is applied vertically upwards.Now the time period is the value of is :

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A sphere of radius has a uniform volume charge density . A spherical cavity of radius whose centre lies at is removed from the sphere.
a. Find the electric field at any point inside the spherical cavity.
b. Find the electric field outside the cavity.
Find the force experienced by a semicircular rod having a charge q as shown in figure. Radius of the wire is R, and the line of charge with linear charge density passes through its center and is perpendicular to the plane of wire.
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An infinite no.of electric charges each equal to are placed along X-axis at and so on. In this setup, if the consecutive charges have opposite sign, then the electric field in newton/coulomb at is:

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