Electrostatics Dpp 010.pdf

(PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere (Pathfinder problem ) ( DPP 10) Q1. Two charged spheres are kept at a finite centre-to-centre spacing as shown in the fi...

(PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere (Pathfinder problem ) ( DPP 10) Q1. Two charged spheres are kept at a finite centre-to-centre spacing as shown in the figure. The force of electrostatic interaction between them is first calculated assuming them point like charges at their respective centres and then force is measured experimentally. If the calculated and the measured values are 𝐹𝑐 and 𝐹𝑚 respectively, which of the following conclusion can you certainly draw? (a) If Fc > Fm for like charges and Fc < Fm for unlike charges, both the spheres must be made of insulating materials. (b) If Fc > Fm for like charges and Fc < Fm for unlike charges, both the spheres must be made of conducting materials. (c) Irrespective of their materials, Fc < Fm for like charges and Fc > Fm for unlike charges. (d) Irrespective of their materials, Fc > Fm for like charges and Fc < Fm for unlike charges. Q2. A thin conducting ring is ruptured when it is given a charge 𝑞. Consider another thin conducting ring, radius of which is 𝑛 times and tensile strength is 𝑘 times of the former ring. How much maximum charge can this second ring be given without rupturing? (a) < 𝑞𝑛𝑘 (b)< 𝑞𝑛√𝑘 (c) < 𝑞𝑛2 √𝑘 (d) Insufficient information Q3. Each of the following figures shows electric field vectors at two points A and B in an electric field. In which figure or figures can the illustrated field be created by a single point charge? (a) (b) (c) (d) INSP (PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere Q4. A positively charged small disc is released on the top of fixed hemispherical frictionless dome in presence of a uniform horizontal electric field. If the disc leaves the dome after an angular displacement 𝜃 = 𝑠𝑖𝑛−1 ⁡(3/5), find ratio of gravitational and electrostatic forces on the disc. Assume that the dome does not exhibit any electrical property. (a) 4/3 (b) 3/4 (c) 9/2 (d) 12 Q5. Two infinitely large planes A and B intersect each other at right angles and carry uniform surface charge densities +𝜎 and −𝜎. Which of the following figures best represents electric field lines? (a) (b) (c) (d) Q6. In the following figures, electric field lines of some electrostatic fields are shown. Which of them are incorrect representations? (a) (b) (c) (d) INSP (PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere Q7. In the figure, a line of electric field created by two point charges q1 and q 2 is shown. If it is known that q1 = 1μC, the charge q 2 is closest to (a) −2μC (b) −4μC (c) −6μC (d) −8μC Q8. A conducting shell of radius R has charge Q. Electrostatic force between two parts of the shell which are on either sides of a plane that is at a distance r(r < R) from the centre of the shell is Q2 r Q2 r (a) 32πε (1 + R) (b) (1 − R) 0 R2 32πε0 R2 Q2 r2 Q2 r2 (c) 32πε 2 (1 + R2 ) (d) 32πε 2 (1 − R2 ) 0R 0R Q9. In another world, instead of the Coulomb's law, electric force ⃗F on a point like charge q due to another point like charge Q is found to obey the following law. Qq(1 − √αr) ⃗F = r 4πε0 r 3 Here α is a positive constant and r is the position vector of charge q relative to the charge Q. Q(1−√αr) (a) Electric field due to a point charge Q is ⃗E = 4πε r3 r 0 (b) Line integral of this electric field ∮⁡E⃗ ⋅ dl over a closed path is also zero as in our world. (c) Gauss' law ∮⁡E⃗ ⋅ ds = qenclosed also holds true for this electric field. ε0 (d) All the above statements are true but this electric field is not conservative INSP (PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere Q10. A straight chain consisting of n identical metal balls is at rest in a region of free space as shown. In the chain, each ball is connected with adjacent balls by identical conducting wires. Length l of a connecting wire is much larger than the radius r of a ball. A uniform electric field E pointing along the chain is switched on in the region. Find magnitude of induced charges on one of the end ball. (a) 2πε0 rnlE (b) 2πε0 r(n − 1)lE (c) 4πε0 r(n − 1)lE (d) 4πε0 (n − 1)2 l2 E Q11. Two identical point charges are moving in free space, when they are 60 cm apart; their velocity vectors are equal in modulus and make angles of 45∘ from the line joining them as shown in the figure. If at this instant, their total kinetic energy is equal to their potential energy, what will be the distance of closest approach between them? (a) 20 cm (b) 30 cm (c) 40 cm (d) 45 cm Q12. A charge particle A is fixed at the base of a uniform slope of inclination α. Another charge particle B is placed on the slope at an angular position β from the line of greatest slope through the position of the first particle. Coefficient of friction between the particle B and the slope is μ(μ < tan⁡ α). For the particle at B to stay in equilibrium, what could be the maximum value of the angle β ? INSP (PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere Q13. One end of an insulating rigid rod of negligible mass and length l is pivoted to a fixed point O. A small ball of mass m having a negative charge of modulus q is attached to the lower end of the rod. Another small ball carrying a positive charge Q is fixed at a height h above the point O as shown in the figure. What should the range of values of mass m of the lower ball be so that the rod remains in a state of stable equilibrium? Acceleration due to gravity is g. Q14. A rigid frame in the shape of a right pyramid is made of conducting rods. The base ABCD is a square and the apex O is vertically above the centre of the base. The frame is electrically neutral. When it is placed in a uniform electric field of intensity E pointing from the corner A towards the corner D, total charges induced on the rods DC and OC are known to be q1 and q 2 respectively. Now the frame is rotated to make the electric field pointing from the corner A towards the corner C. What are the charges induced on each rod? Q15. Three identical thin uniformly charged filaments are fixed along three sides of a cube as shown in the figure. Length of each filament is l and line charge density on each of them is λ. Determine electric field at the centre of the cube. The cube is a geometrical construct and not made of any matter. INSP (PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere Q16. In presence of a uniform horizontal electric field E, a small nonconducting disc of mass m and charge q is released on a non-conducting triangular prism of mass M placed on a frictionless horizontal floor as shown in the figure. Slant face of the prism makes an angle θ with the horizontal and coefficient of friction between it and the disc is μ. If the disc accelerates up the slant face, find acceleration of the prism. INSP (PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere (Answer key) 1. (d) 2.(b) 3.(a,c) 4. (c) 5. (b) 6.(a,b,c) 7. (d) 8. (d) Qqh 9.( a,b) 10. (b) 11.(c) 12. sin−1 ⁡(μcot⁡ α) 13. m > 4πε 3 0 g(h+l) 14. Total charges induced on each of the edges are proportional to their distances from the corner. given in the following table. 15. Zero newton per coulomb (qEsin⁡ θ+mgcos⁡ θ)(sin⁡ θ+μcos⁡ θ) 16. M+msin⁡ θ(sin⁡ θ+μcos⁡ θ) INSP (PHYSICS) ELECTROSTATICS INSP : Click here INSP :Click here INSPwebsite:Clickhere INSP