__LEVEL – I__

__LEVEL – I__

*Q:1. Point charges of magnitude q, 2q and 8q are to be placed on a 9 cm long straight line. Find the positions where the charges should be placed such that potential energy of this system is minimum.*

*[Ans: 2q , 8q at the two ends and q at 3cm from 2q ]*

*Q:2. Water from a metal vessel maintained at a potential of 3 volt falls in spherical drops 2 mm in diameter through a small hole into a thin walled isolated metal sphere of diameter 8 cm placed in air until the sphere is filled with water. Ignoring the thickness of the metal calculate the final potential of the sphere and its electrical energy.*

*[Ans: 4800 V, 512 × 10 ^{-7} J]*

*Q:3. An infinite number of charges each equal to ‘ q ‘ are placed along the x-axis at x = 1, x = 2, x = 4, x = 8, and so on. Find the potential and electric field at the point x = 0 due to this set of charges. What will be the potential and electric field if in the above set up the consecutive charges have opposite sign?*

*Q:Ans: $ \displaystyle \frac{4 k q}{3} $*

*Q:4. A uniform electric field of strength 10 ^{6} V/m is directed vertically downwards. A particle of mass 0.01 kg and charge 10^{-6} coulomb is suspended by an inextensible thread of length 1m. The particle is displaced slightly from its mean position and released.*

*(a) Calculate the time period of its oscillation.*

*(b) What minimum velocity should be given to the particle at rest so that it completes a full circle in a vertical plane without the thread getting slack?*

*(c) Calculate the maximum and minimum tensions in the thread in this situation.*

*[Ans: (a) 0.6 sec (b) 23.42 m/s (c) 6.588, Zero ]*

*Q:5. Two equal charges q are kept fixed at −a and +a along the x-axis . A particle of mass m and charge (q/2)is brought to the origin and given a small displacement along the (a) X-axis and (b) Y-axis. Describe quantitatively the motion in two cases.*

*[Ans: (a) SHM , (b) continue to move up along the Y-axis]*

*Q:6. A strip of length ‘ l ‘ having linear charge density ‘σ ‘ is placed near a negatively charged particle ‘ P ‘ of mass ‘ m ‘ and charge ‘ -q ‘ (as shown in the figure) at a distance ‘ d ‘ from the end ‘ A ‘ of the strip. Find the velocity of ‘ P ‘ as it reaches a point at the distance d/2 from end ‘ A ‘ .*

*Ans: $ \displaystyle v = \sqrt{\frac{\sigma q}{2\pi \epsilon_o m} (\frac{d+2l}{d+l})} $*

*Q:7. A thin fixed ring of radius ‘ R ‘ and positive charge ‘ Q ‘ is placed in a vertical plane. A particle of mass ‘ m ‘ and charge ‘ q ‘ is placed at the centre of ring. If the particle is given a small horizontal displacement, show that it executes SHM also find the time period of small oscillations of this particle, about the centre of ring. (Ignore gravity)*

*Ans: $ \displaystyle T = 2\pi \sqrt{\frac{4 \pi \epsilon_0 m R^3}{q Q}}$*

*Q:8. A non-conducting sphere having a cavity as shown in figure is uniformly charged with volume charge density ρ. Find the potential at a point P which is at a distance of x from C.*

*Ans: $ \displaystyle \frac{4}{3}\pi R^3 k \rho (\frac{1}{x} – \frac{1}{\sqrt{x^2 +R^2/4}}) $*

*Q:9. A particle of charge q and mass m moves along the x-axis under the action of an electric field*

*E = k − c x , where ‘ c ‘ is a positive constant and x is distance from the point, where particle was initially at rest.*

*Calculate :*

*(a) distance travelled by the particle before it comes to rest.*

*(b) acceleration at the moment , when it comes to rest.*

*Ans: (a)2k/c (b) – q k/m*

*Q:10. Charges +q and −q are located at the corners of a cuboid as shown in the figure. Find the electric potential energy of the system.*

*Ans: $ \displaystyle P.E = \frac{k q^2}{a}[2\sqrt{2} – 4 (1+ \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{5}})]$*