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Q.1 In Fig, eight particles form a square, with distance d between adjacent particles. What is the electric potential at point P at the center of the square if the electric potential is zero at infinity? Q.2 Figure shows three sets of cross sections of equipotential surfaces; all three cover the same size region of space. (a) Rank the arrangements according to the magnitude of the electric field present in the region, greatest first. (b) In which is the electric field directed down the page? Q.3 Figure gives the electric potential V as a function of x. (a) Rank the five regions according to the magnitude of the x component of the electric field within them, greatest first. What is the direction of the field along the x axis in (b) region 2 and (c) region 4? Q.4 When charged particles are separated by an infinite distance, the electric potential energy of the pair is zero. When the particles are brought close, the electric potential energy of a pair with the same sign is positive, whereas the electric potential energy of a pair with opposite signs is negative. Give a physical explanation of this statement. Q.5 If the electric field is zero in a particular region of space, what does that tell you about the electric potential in that region? Is the potential zero, or constant, or something else? Explain. Q.6 Will the electric field always be zero at any point where the electric potential is zero? Why or why not? Q.7 Will the electric potential always be zero at any point where the electric field is zero? Why or why not? Q.8 Make sketches of the equipotential surfaces around (a) a point charge, (b) an infinite line of charge, (c) an infinite plane of charge, (d) a finite line of charge, and (e) a charged plate of finite size. Q.9 An electron is released from rest at the origin and moves along the 'x direction. Other experiments show that the electric field is uniform (i.e., constant). Make a sketch showing the direction of the electric field and the equipotential surfaces. Q.10 A particle of positive charge is released from rest and is found to move as a result of an electric force. Does the particle move to a region of higher or lower potential energy? Does the particle move to a region of higher or lower electric potential? Q.11 Repeat Question 6 for an electron. Q.12 A charged particle is released from rest in an electric field. Its motion does not follow the electric field lines. Why? Are there configurations of the electric field that would lead to motion along electric field lines? If so, describe some of them and explain what they have in common. Q.13 Two particles are at locations where the electric potential is the same. Do these particles necessarily have the same potential energy. Explain. Assignment No:4 [Electric Potential] Q.1 Determine the electric potential on the surface of the gold nucleus. The radius of the nucleus is 6.6x10-15m and the atomic number Z=79. [Ans. 1.7x107V] Q.2 The electric potential at 0.9m from a point charge is 50V. What is the magnitude of the charge? [Ans. 5x10-9C] Q.3 A metal wire is bent in the form of circle of radius 10cm. It is given a charge of 200µC, which spreads uniformly on it. Calculate the electric potential at the center. [Ans. 18x106V] Q.4 The electric field at a point due to point due to point charge is 20N/C and the electric potential is 10V. Calculate the distance of point from the charge and the magnitude of the charge. [Ans. 0.5m, 0.55x10-9C] Two points A and B are located in diametrically opposite directions of point charge of 2µC at distance of 2m and 1m respectively from it. Determine the potential difference between the two points. [Ans. –9x103V] Q.5 Q.6 A regular hexagon of side 10cm has a charge of 5µC at each of the vertices. Calculate the potential at the center of the hexagon. [Ans. 2.7x106V] Q.7 Two charges 3µC and -2µC are located 15cm apart. At what point on the line joining the two charges is the electric potential zero. [Ans. 9cm] Two tiny spheres carrying charges 1.5µC and 2.5µC are located 30cm apart. Find the potential [a] at the mid point of the line joining the two charges [b] at a point 10cm from this mid point in a plane normal to the line and passing through the mid point. [Ans. 2.4x104V, 2 x105V] Q.8 Q.9 ABC is right angles triangle, where AB and BC are 25cm and 60cm respectively; a metal sphere is placed at B. Find the amount of work done in carrying a positive charge of 1C from C to A. [Ans. 0.042J] Q.10 Positive charges 6,12 and 24nC are paced at the three vertices of a square. What charge must be placed at the fourth vertex so that the total potential at the center of the square is zero? [Ans. –42nC] Q.11 Eight charged drops of water, each of radius 1m and having a charge of 10-10 C, combine to form a bigger drop. Determine the potential of the bigger drop. [Ans. 3600V] Q.12 A uniform electric field of 20N/C exists in the vertically downward direction. Determine the increase in electric potential as one goes through a height of 50cm. [Ans. 10V] Q.13 A uniform electric field of 30N/C exists along the x-axis. Calculate the potential difference between B and A if A [4,2] and B[10,5]. [Ans. –180V] Q.14 A charge Q is distributed over two concentric hollow spheres of radii r and R where R > r such that the surface charge densities are equal. Find the potential at the common center. Q(R + r ) 2 2 [Ans. 4πε 0 R + r ( ) ] Q.15 An infinite number of charges q each are placed along x axis at x=1, x=2, x=4…..[a] find the electric potential at the origin. [b] What will be the potential if the consecutive charges have opposite sign and charge at x=1 is positive. [Ans. q/2πε0, q/6πε0]

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