Tiêu đề 01 ELECTRIC FORCE, FIELD, FLUX, GAUSS LAW.pdf ✅

ASSIGNMENT-1: ELECTRIC FORCE, FIELD, FLUX, GAUSS LAW 1 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 CSIR-UGC-NET | GATE PHYSICS ELECTROMAGNETIC THEORY ASSIGNMENT-1 : ELECTRIC FORCE, FIELD, FLUX, GAUSS LAW OBJECTIVE QUESTIONS 1. Consider two point charges q and q located at the points, x = a and x a   , respectively. Assuming that the sum of the two charges is constant, what is the value of for which the magnitude of the electrostatic force is maximum ? [JEST 2015] (a) μ (b) 1 (c) 1/μ (d) 1+μ 2. Two points charges +q1 and +q2 are fixed with a finite a distance ‘d’ between them. It is desired to put a third charge q3 in between these two charges on the line joining them so that the charge q3 is in equilibrium. That is: (a) Possible only if q3 is positive (b) Possible only if q3 is negative (c) Possible irrespective of the sign of q3 . (d) Not possible at all. 3. Three positively charged particles lie on a straight line at positions 0, x and 10 as indicated in the figure below. Their charges are Q, 2Q and 4Q cm respectively. Q 2Q 4Q 0 x 10 If the charges at x = 0 and x = 10 are fixed and the charge at x is movable, the system will be in equilibvrium when x = (a) 8 (b) 2 (c) 20/3 (d) 10/3 4. Two point charges Q1 = 1 nC and Q2 = 2 nC are kept in free space such that the distance between them is 0.1 m. [GATE 2001] (a) The force on Q2 is along the direction from Q2 to Q1 (b) The force on Q2 is the same in magnitude as that on Q1 (c) The force on Q1 is attractive (d) A point charge Q3 = –3 nC, placed at the midpoint between Q1 and Q2 , experiences no net force. 5. When a particle of charge q is at rest, it produces (a) Only electric field (b) Only magnetic field (c) Both electric and magnetic fields. (d) A magnetic field depending upon the sign of the charge. 6. An electric field in a region is given by   E x, y,z axi czj 6byk. ˆ ˆ ˆ     For which of a, b, c does this represent an electrostatic field ? [JEST 2012] (a) 13, 1, 12 (b) 17, 6, 1 (c) 13, 1, 6 (d) 45, 6, 1 7. If 1 ˆ ˆ ˆ E xyi yzj xzk    2 3  and 2 2 2 ˆ ˆ ˆ E y i xy z j yzk     (2 ) 2  then [JEST 2013] (a) Both are impossible electrostatic fields. (b)Both are possible electrostatic fields. (c) Only E1  is a possible electrostatic field. (d)Only E2  is a possible electrostatic field.
2 ASSIGNMENT-1: ELECTRIC FORCE, FIELD, FLUX, GAUSS LAW North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 8. Which of the following force fields is/are conservative ? I. 3 2 2 4 2 2 3 3 (4 3 ) ( 3 ) 2 ( ) x y x z x y z z x y      i j k II. 4 5 4 2 3 4 5 ( ) ( ) ( ) yz x x z x y x y z      i j k III. 2 2 4 3 2 2 x xy z z x y z yz x (3 4 ) ( 2 ) 2 (2 3 )      i j k (a) II and III only (b) I, II and III (c) I and III only (d) I and II only (e) I only 9. Which of the following vector fields can represent an electrostatic field? (a)       2 2 2 ˆ ˆ ˆ 2 2 2 xz y i xy z j yz x k      (b) ˆ ˆ ˆ xyi yzj xzk   2 3 (c) ˆ ˆ ˆ yzi xzj xyk   (d)     2 2 2 ˆ ˆ ˆ y i xy z j yz x k     2 2 (e)   2 2 ˆ ˆ ˆ y i xy z j yzk    2 2 10. Three charges are located on the circumference of a circle of radius ‘R’ as shown in the figure below. The two charges Q subtend an angle 90o at the centre of the circle .The charge ‘q’ is symmetrically placed with respect to the charges Q. If the electric field at the centre of the circle is zero, what is the magnitude of Q? Q Q q [NET Dec. 2012] (a) q/ 2 (b) 2q (c) 2q (d) 4q 11. A charge distribution has the charge density given by 0 0        Q x x x x { ( ) ( )}. For this charge distri- bution the electric field at 0 (2 ,0,0) x [GATE 2013] (a) 2 0 0 2 ˆ 9 Qx  x (b) 3 0 0 ˆ 4 Qx  x (c) 2 0 0 ˆ 4 Qx  x (d) 2 0 0 ˆ 16 Qx  x 12. A segment of a circular wire of radius R, extending from 2 0 to    , carries a constant linear charge density, . The electric field at origin ‘O’ is: y x O R (a)   0 x y ˆ ˆ 4 R     (b) 0 1 1 x y ˆ ˆ 4 R 2 2           (c) 0 1 1 x y ˆ ˆ 4 R 2 2           (d) 0 13. Consider the plane defined by x, y, z 10 m   . If it carries a charge of 2 20 nC/m , what is the electric field intensity at the origin? (a) ˆ V –720 k m  (b) ˆ V –360 k m  (c) ˆ V –72 k m  (d) ˆ V –18 k m 
ASSIGNMENT-1: ELECTRIC FORCE, FIELD, FLUX, GAUSS LAW 3 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 14. A very circular wire of radius a carries electric charge of uniform liner density  . On its axis, the magnitude of the electric field attains its maximum value at a perpendicular distance d form the plane of the wire (see the figure below). The value of d is d a (a) 0 (b) 0.32 a (c) 0.50a (d) a/ 2 15. A circular loop of radius R, carries a uniform line charge density . The electric field, calculated at a distance z directly above the center of the loop, is maximum if z is equal to, [JEST 2015] (a) 3 R (b) 2 R (c) 2 R (d) 2R 16. A particle of mass m and charge q is constrained to move along a straight line joining two other equal charges q fixed at x a   . The time period of small oscillation is: (a) 0 2 a T am q    (b) 0 4 a T am q    (c) 0 a T am q   (d) 0 2 a T am q    17. A point charge ‘q’ sits at a corner of a cube of side ‘a’, as shown in the figure on the right. The flux of the electric field vector through the shaded side is [TIFR 2013] q (a) 0 q 8 (b) 0 q 16 (c) 0 q 24 (d) 0 q 6 18. Consider a set of two stationary point charges q1 and q2 as shown in the figure. Which of the following statements is correct? [GATE 2002] Contour C Surface S q2 q1 P (a) The electric field at P is independent of q2 (b) The electric flux crossing the closed surface S is independent of q2 (c) The line integral of the electric field E  over the closed contour C depends on q1 and q2 . (d)   .E 0   everywhere 19. The flux of electric field through a circle of radius R placed in the x-y plane with its centre at the origin due to a point charge Q placed at (0, 0, d) is d x y Q R
4 ASSIGNMENT-1: ELECTRIC FORCE, FIELD, FLUX, GAUSS LAW North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 (a)   1/2 0 2 2 1 2             Q d d R  (b)   3 3/2 2 0 2 2  Q d d R  (c) 0 4 Q d  R (d) 2 2 0 4 Q R  d 20. An electron field     1 ˆ E r arˆ sin cos r        exists in space. What will be the total charge enclosed in a sphere of unit radius centered at the origin? (a) 0 4 a (b)   0 4    (c)   0 4    (d) 0 4  21. Consider a charge Q at the origin of 3-dimensional coordinate system. The flux of the electric field through the curved surface of a cone that has a height ‘h’ and a circular base of radius R (as shown in the figure) is h R Q (a) 0 Q  (b) 0 2 Q  (c) 0 hQ R (d) 0 2 QR h  [NET Dec. 2015] 22. The potential due to an electric dipole p placed at the origin is known to be of the form   3  r p r r  . / . The total flux of the electric field through a spherical surface of radius R with the dipole at the centre is given by (a) Zero (b) 2 3 p R   (c) 2 3 p R   (d) 4 3 p R   23. The total outward electric flux going from a cube with 0 1, 0 1, 0 1       x y z metres containing a volume charge density   16 xyz , will be (a) 16 (b) 8 (c) 4 (d) 2 24. The charge density as a function of the radial distance r is given by [JEST 2018]   2 2 0 2 R r r R     for r < R and zero otherwise. The electric flux over the surface of an ellipsoid with axes 3R, 4R and 5R centred at the origin is (a) 3 0 0 4 3  R  (b) 3 0 0 8 9  R  (c) 3 0 0 8 15  R  (d) 0 25. A non-conducting thin ellipsodial shell defined by the equation 2 2 2 2 x y z a    2 3 has a net chareg Q spread uniformly over its surface. The flux passing through a hemispherical surface defined by 2 2 2 2 x y z a z     and 0, is [NET Dec. 2019] (a) Q / 3  0  (b) 0 Q/  (c)   0 Q / 2 (d)   0 Q / 3 26. Consider a hollow charged shell of inner radius ‘a’ and outer radius ‘b’. The volume charge density is   2 k r r   (where k is a constant) in the region a < r < b. The magnitude of the electric field produced at distance r > a is: [NET Dec. 2012]