DEPARTMENT OF ELECTRONICS ENGINEERINGWalchand Collegeof Engineering, Sangli Class: - T.Y. B.Tech. (Electronics Engineering) Semester-II 2015-2016 Course: - Electromagnetic Engineering: 2EN 321 Tutorial-1 Q.1 Q.2 Q.3 Q.4 Q.5 Q.6 A charge QA = 20 C is located at A( 6, 4, 7),and a charge QB = 50 C is at B(5, 8, 2) in free space. If distances are in meters, Find:a)RAB; b)RAB;c)Determine the vector force exerted on QAby QB if 0 = 8.85 10 12 F/. (Ans. 11ax+ 4ay 9azm;14.76 m; 30.72ax+11.169 ay 25.13azmN) Four 10nC positive point charges are located in the z = 0 plane at the corners of a square 8 cm on a side. A fifth 10nC positive charge is located at a point 8 cm distant from the other charges. Calculate the magnitude of the total force on this fifth charge for = 0. (Note:-If the square is assumed to be placed such that its centre is origin (0, 0, 0) i.e. 4 cm < x, y < 4 cm, then F = 4 10 4 N) Point charges of 50 nC each are located at A(1, 0, 0), B( 1, 0, 0), C(0, 1, 0) and D(0, 1, 0) in free space. Find the total force on the charge at A. (Ans. 21.5 ax N) Find the force on a charge q = 1 nC located at the mid-point of two equal charges of 1 C located at (1, 1, 1)m and (5, 3, 2)m in free space. Point charges 5 nC and 2 nC are located at (2, 0, 4)m and ( 3, 0, 5)m respectively. a) Determine the force on a 1 nC point charge located at (1, 3, 7)m. b) Determine the electric field at (1, 3, 7)m. (Ans. 1.004 ax 1.284 ay + 1.4 aznN; 1.004 ax 1.284 ay + 1.4 az V/m) Three point charges are positioned in the x-y plane as follows: 5 nC at y = 5cm, −10 nC at y = −5 cm, and 15 nC at x = −5 cm. Find the required x-y coordinates of a 20nC fourth charge that will produce a zero electric field atthe origin. Note: - The total electric field produced by three point charges should be equal in magnitude and opposite direction to that of electric field produced by 20 nC point charge at origin. (Ans. (3.43 cm,−3.43 cm) ) 2EN321: EME Sem-II/2015-16 ELN/ WCE, Sangli 1/5 10 J. 1). 1. 0) to A(0.2 Q. (a) Find Q0.3 Q. 10. z = 0 in the field E = : (a) 5 ax V/m. 529 V. 1)m. find E at (a) PA(r = 0. (c) 12 nC/m on the line y = 2. 4). .6 Q. Determine the potential and electric field intensity at (1. (c) 5x ax + 5y ay V/m. Find E at: (a) PA(0. 45azV/m. z = 0. 20. (b) point charge of 18 nC at (1. 0. 4). (b)Find E atM (1. Find V at the point (1. 30.2 V. (Ans. 2.5)m. 20 J. Calculate V1 if point P1 is located at P1 ( 2.2. (Ans. 2.8ay+ 36.3 V) Calculate the work done in moving a 4 C point charge from B(1. 3. 2. 30 J ) If we take zero reference for potential at infinity.5).2 m. 3. 1). 6.1 Q. (a) V = 0 at (6.4 V ) The electrostatic potential in free space is given by V = 5xy2 + 10yz2 Volts. 4). 67.89 V) A point charge of 4 nC is situated at the origin and another point charge of 6 nC is located at the point (3. z =0.6. 1) and. 1)m. 8. 2. (b) PB (r = 0. 3. 0. 1. z = 0. (Ans.67 V.1 kV/m. 2. (b) 5x ax V/m. ( Ans.0 V.5 Q.1 kV/m) A 15 nC point charge is at origin in free space. and is zero elsewhere.53 az V/m. ( Ans. (b) V =0 at infinity.11ax 180.63 C.53 az V/m) Given the surface charge density. 0. existing in the region r < 0. 4). 0) along the path y =2 2x.5).5 m. 1. 183. (Ans. 10. 8.9azV/m) A charge Q0 located at the origin in free space produces a field for which Ez =1kV/m at point P( 2.7 Infinite uniform line charges of 5 nC/m lies along the (positive and negative) x and y axes in free space.12ar 150. Sangli 2/5 . 2) caused by the charge configurations in free space: (a) 12 nC/m on the line.5. 5) in rectangular and cylindrical coordinates. 5. 43. find the potential at (0. r = 2. (c) V = 5 V at (2. 0.63 ay 150. z = 0. Note: V1= VP12 + VP2 ( Ans.Tutorial-2 Q. (b) PB(0. z = 0. 2EN321: EME Sem-II/2015-16 ELN/ WCE.4 a) b) Q. 36. s = 2 C/m2. E = 1. 6) produced by: (a) a point charge QA = 55 mC at Q( 2. (a) Find the total electric flux passing through the rectangular surface z = 2.1 Q. Both lines are 8-m above ground. (Ans. 1.4 ay kV/m.5 ar V/m.61 kV/m) A uniform line charge of 2 C/m is located on the z-axis.3 Q. (b) 4 z 4. 305 nC. 60 az C/m2) In free space. =250. (c) a uniform surface charge density SC = 120 C/m2 on the plane z = 5 m. (b) Find E at P (2. 7.4 Q. (c) Find an approximate value for the total charge contained in an incremental sphere located at P (2.57ay + 19.38 10 21 C) Given the electric flux density.2 Q. (a) find E at point P( r = 2. in the az direction. 1 < y < 3. Sangli 3/5 . 6. 1.14az C/m2.9az kV/m) 2EN321: EME Sem-II/2015-16 ELN/ WCE. (Ans. 3) if the charge exists from: (a) < z < . (Ans.5 Q. 360 C. 3.3 r2 ar nC/m2 in free space. 212ay + 424az C/m2. = 900).4ax + 146. 0<z < 5 m.2 ax + 14.4 ay 195. 3). (b) find the total charge within the sphere r =3 m. 360 C) Two long parallel conductors of a dc transmission line separated by 2-m have charge l = 5 µC/m of opposite sign.Tutorial-3 Q. 6).6 Calculate D in rectangular coordinates at point P (2. What is the magnitude of electric field E. 146. (b) a uniform line charge LB = 20 mC/m on the x axis. (c) find the total electric flux leaving the sphere r =4.38ax 9. (Ans. 4-meters directly below one of the wire? r = 1. D = 0. 135. 0 < x < 2. let D = 8xyz4ax + 4x2z4ay + 16 x2yz3az pC/m2. 4.8ay + 4. (Ans. 3. (Ans. 1365 pC.9ax + 9. 3) and having a volume of 10 12m3. Find E in rectangular coordinates at P (1. 2. 2. 965 n C) Let D = 4xy ax + 2 (x2 + z2) ay + 4 yz az C/m2 and evaluate the surface integrals and volume integral of the divergence theorem to find the total charge enclosed in the rectangular parallelepiped 0 < x < 2.2 az V/m. 0 < y < 3. 0) in the field of two current filaments. v) the total magnetic flux outside the conductor.2 Q. 1 y 1.08 A in the az direction at x = 0.2 mT. (Ans. and the total current in the az direction is 20 A.6 Express the value of H in the Cartesian components at P (0.01. 57 A/m2 ) Evaluate both sides of the Stokes’ theorem for the field H = 6xy ax – 3y2ay A/m and the rectangular path around the region.82ay A/m) Find H at the centre of a square current loop of side 4 m if a current of 5 amp is passing through it. 126 A ) 2EN321: EME Sem-II/2015-16 ELN/ WCE. iii) the total magnetic flux per unit length inside the conductor. 2 x 5.Tutorial-4 Q. z = 0.5 mm. H = 4 0. (Ans. ii) Determine the quotient of the closed line integral and the area enclosed by the path as an approximation to ( H )y. 354 A. (Assume the direction of current is clockwise. iv) the total flux for r < 0. 1). the conductor axis lies on the z axis. (Ans. 126 A. 0. 0. Sangli 4/5 . iii) Determine ( H )y at the center of the area.5 Q. 0.5 r 2 and 0 z 3 m. (Assume infinitely long straight current filaments) (Ans. 1) to P4(2.08 A in the az direction on the z-axis and 0. 3.5 µWb/m.796ax+ 0. 4) to P3(4. 4) to P2(4. 59 A/m2.5 mm. Use Biot-Savart law to find H at P(0. If the radius a = 1 mm. 1 = 450. 3.64 wb ) A filamentary current of 10 A is directed in from infinity to origin on the positive xaxis.1252 a A/m ) Find the magnetic flux ( ) crossing the plane surface defined by 0. y = 0. 2 = 450.1 Q. 16.015. 1) to P1. 2 µWb/m. if B = (4/r) a Tesla. 3. (Ans.8 mm.2813 = 1. then according to the right hand thumb rule. 3. 3. (Ans. 3.3 a) b) Q. ii) B at r = 0.4 Q. Let the positive direction of dS be az. 1592 A/m. ) i) Evaluate the closed line integral of H about the rectangular path P1(2. the direction of H is into the plane of current loop) Note: Use Biot-Savart Law for the finite current element) (Ans. 0. 0. and then back out to infinity along the positive y-axis.796ay A/m ) A solid conductor of circular cross section is made of a homogeneous nonmagnetic material. given H = 3z ax – 2x3 az A/m. find: i) H at r = 0. (ii) E = 3 ax + 4 ay + 6 az kV/m. are located in free space.30 az. 48 ay + 36 azmN. 2016 2EN321: EME Sem-II/2015-16 ELN/ WCE. 37524 sin(2 t) Volts. 0) and I2ΔL2 = 3 10 6( 0.1 Q. 120 [cos( ct) – sin( ct)] mA ) The point charge Q = 18 nC has a velocity of 5 106 m/s in the direction av = 0. (iii) B and E acting together. Find I(t) if B = (i) 0. emf = 0. 5.333 ay 2. 6).3 cos(120 t – 300) az Tesla.4 ay + 0.67 ax + 0. (Ans.75 ay + 0. 1.3 a) b) c) A circular loop of 10 turns of conducting wire of radius r = 5 cm and resistance R = 10 is placed in a slowly varying uniform magnetic field. (Ans. Find the vector force on: (i)I2ΔL2 by I1ΔL1 . (4.333 ax + 0.667az)10 20N ). given A(1. 1. ( 1.060 ax + 0.2 Q. Find the vector force exerted on a straight wire carrying 12 A in the aAB direction. (Ans. 660 µN. (ii) 0. Q. Sangli 5/5 . 140 µN. Calculate the magnitude of the force exerted on the charge by the field: (i) B = 3 ax + 4 ay + 6 az mT.4 cos [ (ct – y)]azµTesla. 2 . (ii)B(3. (Ans. where c = 3 108 m/s. as shown in the figure. Find the emf and current generated in the loop.5 ax + 0. The magnetic field makes an angle of 450 with respect to the direction of the surfaces of the loop.037524 sin(2 t) Amp ) A perfectly conducting filament containing a small 500 resistor is formed into a square. The magnitude of magnetic field is given by B = cos (2 t) Tesla.3 az) A m at P2(2.Tutorial-5 Q. I1ΔL1 = 3 10 6 ay A m at P1(1. 1) and (i)B(2. 2 ). 670 µN ) The field B = 2 ax + 3 ay + 4 azmT is present in free space.4 Date of Submission: 23 Feb. 1). (Ans.67az)10 20N.(ii)I1ΔL1by I2ΔL2. I = 0. 12 ax 216 ay + 168 azmN) Two differential current elements. 57 sin(120 t – 300) mA. 0.