Charge q is uniformly distributed over a thin half-ring of radius R. The electric field at the centre of the ring is 

(1) q2π2ε0R2

(2) q4π2ε0R2 

(3) q4πε0R2

(4) q2πε0R2

Concept Questions :-

Electric field
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In the given figure two tiny conducting balls of identical mass m and identical charge q hang from non-conducting threads of equal length L. Assume that θ is so small that tanθsinθ, then for equilibrium x is equal to 

(1) q2L2πε0mg13

(2) qL22πε0mg13

(3) q2L24πε0mg13

(4) q2L4πε0mg13

Concept Questions :-

Coulomb's law
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Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in 

(1)   (2)

(3)    (4)

Concept Questions :-

Electric field
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Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when 

(1) x=d2

(2) x=d2

(3) x=d22

(4) x=d23

Concept Questions :-

Coulomb's law
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An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is 

(1) pEI1/2

(2) pEI3/2

(3) IpE1/2

(4) pIE1/2

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An infinite number of electric charges each equal to 5 nano-coulomb (magnitude) are placed along x-axis at x = 1 cm, x = 2 cm, x = 4 cm, x = 8 cm ………. and so on. In the setup if the consecutive charges have opposite sign, then the electric field in Newton/Coulomb at x = 0 is 14πε0=9×109Nm2/c2

(1) 12 × 104

(2) 24 × 104

(3) 36 × 104

(4) 48 × 104

Concept Questions :-

Electric field
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A small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L. Time period of pendulum is T0. When parallel plates are charged, the time period changes to T. The ratio T/T0 is equal to 

(1) g+qEmg1/2

(2) gg+qEm3/2

(3) gg+qEm1/2

(4) None of these 

Concept Questions :-

Electric field
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Three charges –q1, +q2 and –q3 are placed as shown in the figure. The x-component of the force on –q1 is proportional to 

(1) q2b2q3a2sinθ

(2) q2b2q3a2cosθ

(3) q2b2+q3a2sinθ

(4) q2b2+q3a2cosθ

Concept Questions :-

Electric field
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Two-point charges +q and –q are held fixed at (–d, 0) and (d, 0) respectively of a (x, y) coordinate system. Then 

(1) E at all points on the y-axis is along i^

(2) The electric field E at all points on the x-axis has the same direction

(3) Dipole moment is 2qd directed along i^

(4) Work has to be done in bringing a test charge from infinity to the origin

Concept Questions :-

Electric dipole
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A point charge of 40 stat coulomb is placed 2 cm in front of an earthed metallic plane plate of large size. Then the force of attraction on the point charge is

(1) 100 dynes

(2) 160 dynes

(3) 1600 dynes

(4) 400 dynes

Concept Questions :-

Coulomb's law
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