106Q1.
Let the charge given to the bob be Q.
The string will become loose when T=0
i.e. mg = kQq/x2
Put the reqd values
m=0.1 kg, g≈10m/s2, k=9x109, q = 2*10-4 and x = 0.1 m. then u can find Q
H.C.Verma doubts
1) A particle having a charge of 2.0 X 10-4 C is placed directly below and at a separation of 10 cm from the bob of a simple pendulum at rest. The mass of the bob is 100g. What charge should the bob be given so that the string becomes loose.
2) Two particles A and B each having a charge Q are placed at a distance d apart. Where should a particle of charge q be placed on the perpendicular bisector of AB so that it experiences maximum force? What is the magnitude of this maximum force?
3) The bob of a simple pendulum has a mass of 40g and a positive charge of 4.0 X 10-6 C. It makes 20 oscilliations in 45 s. A vertical electric field pointing upward and of magnitude 2.5 X 104 N/C is switched on. How much time will it now take to complete 20 oscilliations?
4) A charge Q is placed at the centre of a cube.Find the flux of the electric field through the six surfaces of the cube?
5) A non-conducting sheet of large surface area and thickness d contains uniform charge distribution of density Ï.Find the electric field at a point P inside the plate,at a distance x from the central plane.Draw a qualitative graph of E againt x for 0<x<d.
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5 Answers
15) its given a non conducting sheet of large surface area,so we can assume length to be infinite and the central plane is parallel to length. take a cuboid bisected by the central plane,as the gaussian surface.
thus,gaussian cuboid is at equal distance x from central plane on both sides.so length of gaussian cuboid is 2x.
now, 2EA =(A 2x) K
SO, E=Kx/Eo here taken k in place of row.
14) here, a pt. charge is kept at the centre.so,the flux through each surface would be symmetrically q/6Eo.so the flux though six surfaces is q/Eo
12) . d .
Q Q
thus,for maximum force, the third charge should be placed outside the distance d(otherwise two charges would give oppositely directing forces). let q be placed x distance from one of the Q.then put equations for both forces,and let total force u got is F.
then put ∂F/∂x to get distance,charge and then maximum force.
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