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Electric Charge And Field 1 Mark 1. Define dipole moment of an electric dipole. Is it a scalar or a vector? Electric dipole moment of an electric dipole is equal to the product of either charge and distance between the two charges. It is a vector quantity. 2. Why must electrostatic field be normal to the surface at every point of a charged conduction? The component of electric field along the tangent to the surface of the conductor must be zero π¬ ππ¨π¬ π½ = π where ΞΈ is angle between and tangent to the surface. As Eβ π or ΞΈ = 900 Hence E is perpendicular to the surface 3. A proton is placed in a uniform electric field directed along the position x-axis. In which direction will it tend to move? Proton will tend to move along X axis in the direction of electric field. 4. Why do the electric field lines not form closed loop? No electric field exist from negative to p[ositive charge , hence electric field lines do not form closed loop. 5. In which orientation a dipole placed in a uniform electric field is in a) Stable, b) Unstable Equilibrium? (a) For stable equilibrium the angle between p and E must be 00 (b) For unstable equilibrium the angle between p and E must be 1800 2 Marks 1. Charges of magnitudes 2Q and βQ are located at points (a, 0, 0) and (4a, 0, 0). Find the ratio of the flux of electric field due to these charges through concentric sphere as of radii 2a and 8a centered at the origin. 2. Ans: Ρ1 Ρ2 2π = 2πβπ = 2 1 2. Two Charges of magnitudes -3Q and +2Q are located at points (a, 0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius 5a with the centre at the origin? 2. Ans: Ξ¦E = β3π+2π β0 = π β0 . 3. Two concentric spherical shell of radii R and 2R are given charges Q1 and Q2respectively. The surface charge densities on outer surface are equal. Determine the ratio of charges Q1 and Q2. 2. Ans: π1 π2 = 4ππ 2 4π(2π )2 = 1 4 4. Define electric field intensity. Write its SI unit. Is it scalar or vector? 2. Ans: Electric field intensity E can be defined as the force experienced per unit charge at that point. Its SI unit is N/C. It is a vector quantity. E = π π 5. Force of attraction between two point charges placed at a distance d is F. What distance apart should they be kept in the same medium so that the force between them is F/3? 2. 1|Page Ans: πΉβ² πΉ = π2 π21 or πΉ 3πΉ = π2 β΄ d1 = β3 d π21 π 6. Plot a graph showing the variation of Coulombβs force F versus π , where r is the distance π between the two charges (1µC, 2µC) and (2µC -3µC) . Interpret the graphs obtained. Ans: Coulombβs force between two charges q1 and q2 separated by a distance r is given by 1 F πΌ q1.q2 and F πΌ π2 . F is repulsive between like charges (1µC, 2µC) and F is attractive between unlike charges ((2µC, -3µC) Attractive 1 π2 Repulsive 7. An electric dipole moment 4 x 10-9 cm is aligned at 300 with the direction of a uniform electric field of magnitude 5 x 104 N/C. Calculate the magnitude of the torque acting on the dipole. Ans: 1 π = PE sinπ = 4 x 10-9 x 5 x 104 x sin300 = 4 x 10-9 x 5 x 104 x = 1 x 10-4 Nm. 2 8. Two fixed point charges +4e and +e units are separated by a distance a. Where a third charge q should be placed for it to be in equilibrium? +4e ----------- x -------------------(a-x)-------- e 1 4π π₯ π 4ππ0 π₯2 = 1 ππ₯π 4ππ0 (πβπ₯)2 or 4(a-x)2 = x2 or 2(a-x) = x β΄x = 2π 3 3 Marks 1. a) A point charge (+Q) is kept in the vicinity of uncharged conducting plate. Sketch electric fieldlines between the charge and the plate. (b) Two infinitely large plane thin parallel sheets having surface charge densities Ο1 and Ο2(Ο1 > Ο2 ) are shown in the figure. Write the magnitudes and directions of the net fields in theregions marked II and III. (a) The lines of force start from + Q and terminate at metal place inducing negative charge on it. The lines of force will be perpendicular to the metal surface. 2|Page (b) (i) Net electric field in region II π π π¬ = (ππβ ππ ) Direction of electric field in from sheet A to sheet B. (ii) Net electric field in region III π π π¬ = (ππ+ ππ )Direction is away from the two sheets i.e. towards right side. 2. Given a uniform electric field E = 5 × 103i N/C, find the flux of this field through a square of 10 cm on a side whose plane is parallel to the y-z plane. What would be the flux through the same square if the plane makes a 30° angle with the x-axis? 3. Deduce the expression for the torque acting on a dipole of dipole moment p in the presence of a uniform electric field E . 3|Page 4. (a)A point charge +10 ΞΌC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. What is the magnitude of the electric flux through the square? (b) If area of this square is reduced to half, what will be the new electric flux? Ans: 5. Write any three properties of electric lines of force. Ans: (i) They originate from positive and terminate at negative charge. (ii) Electric field lines never intersect each other. (iii) Electric field lines of similar charges exert lateral pressure. 4|Page 5 Marks 1. Derive expression for electric field at a point on the axial line of the dipole. Give the direction of electric field at the point. Ans: The axial line of a dipole is the line passing through the positive and negative charges of the electric dipole. 5|Page 2. An electric dipole is held in uniform electric field (i) Show that no translator force acts on it. (ii) Derive an expression for the torque acting on it. Ans: 3. State Gauss Theorem. A thin charged wire of infinite length has line charge density βΞ»β. Derive expression for electric field at a distance βrβ. Ans: 6|Page 4. Charge q is distributed uniformly on a spherical shell of radius R. Using gauss law derive expression of electric field at a distance r from the centre when (i)r>R (ii) r=R (iii) r<R Ans: Consider a hollow conducting sphere of radius R with its centre at O. let Ο be its surface density. The field at any point P, outside or inside depends upon the distance from the centre of the spherical shell. Let the distance between the centre of the spherical shell and the point be r. 7|Page 8|Page