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Curl of a rotation field Compute the curl of the rotation field
F = a x r, where a = ⟨2, -1, 1⟩ and r = ⟨x, y, z⟩(see figure). What are the
direction and the magnitude of the curl?
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- Use the following constants if necessary. Coulomb constant, k = 8.987 × 10º N - m² /C&acuum permitivity, €o = 8.854 × 10-12 F/rMagnetic Permeability of vacuum, Ho = 12.566370614356 ×x 10-7 H/rMagnitude of the Charge of one electron, e = -1.60217662 × 10-19 CMass of one electron, me = 9.10938356 × 10-31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb Calculate the magnetic field created by an infinite wire carrying current I = 17 mAurrent at a distance r from the wire B field at r = 13 cm Give your answer up to at least three significance digits. T B field at r = 130 cm Give your answer up to at least three significance digits. TQ/Let auniform surface chargedensity of 5nc/m be present at z= oplane, auniform line chargedausity o8 nc/m be locatedat x=0,2=4 a point chargeof 2 Hcbe tresent at p(e,ojol. If vso at (9,5), find Vati, 2,3)? Ans: 1-98 kvPlease check my solution.
- Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m² /Cacuum permitivity, €o = 8.854 x 10-12 F/rMagnetic Permeability of vacuum, lo = 12.566370614356 x 10-7 H/@harge of one electron, e = -1.60217662 x 10-19 CMass of one electron, me = 9.10938356 × 10-31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulonmh Part I The following figure shows 3 resistors R1 = 22 kN R2 = 3.3 kN R3 = 2.2 klconnected to a battery source emf E = 10 volts Ri a Rz Rg a)Find the current across R3.Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m2 /CVacuum permitivity, Eg = 8.854 x 10-12 F/rMagnetic Permeability of vacuum, n = 12.566370614356 x 10-7 H/rMagnitude of the Charge of one electron, e = -1.60217662 x 10-19 CMass of one electron, m, = 9.10938356 x 10-31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µC'means microcoulomb In the figure the blue region represents a magnetic field B = 3.3 Tand the green region represents a magnetic field B2 = 6.0TA particle with charge q= 4.4 µG mass m = 0.065 granand velocity v = 35 m/ravels toward the blue region as shown in the figure. b)Draw a schematic diagram to show the direction of the force for this system.Use the following constants if necessary. Coulomb constant, k = 8.987 × 10º N - m² /C&acuum permitivity, €o = 8.854 × 10-12 F/rMagnitude of the Charge of one electron, e = 1.60217662 × 10-19 CMass of one electron, me = 9.10938356 × 10-31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb 93 a a Consider The rectangular arrangement of four point charges shown in Figure 1, where they lie on the corners of the rectangle where q = 19 nC q2 = 43 nCq3 = 27 nCand q4 = -22 nand a = 21 cm a)Calculate how much work is required to set up the arrangement if the charges are initially infinitely far apart and were at rest. (Hint: Use the relation between work done by the external agent and total electrical potential energy of the system) Net workdone Give your answer to at least three significance digits. joules b)Calculate the potential at the centre of the square due to all four charges. Potential at the center Give your answer to at least…
- Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m2 /CVacuum permitivity, Eg = 8.854 x 10-12 F/rMagnetic Permeability of vacuum, n = 12.566370614356 x 10-7 H/rMagnitude of the Charge of one electron, e = -1.60217662 x 10-19 CMass of one electron, m, = 9.10938356 x 10-31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µC'means microcoulomb In the figure the blue region represents a magnetic field B = 3.3 Tand the green region represents a magnetic field B2 = 6.0TA particle with charge q= 4.4 µG mass m = 0.065 granand velocity v = 35 m/bravels toward the blue region as shown in the figure. c) Calculate the angular frequency of the particle when it is in the blue and when it is in the green region. What will happen to the angular frequency in the blue region if we double the velocity of the particle? angular frequency in blue region Give your answer up to at least three significance digits. rad/s angular frequency in green…Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m2/Cacuum permitivity, €o = 8.854 × 10-12 F/rMagnitude of the Charge of one electron, e = -1.60217662 x 10-19 CMass of one electron, m, = 9.10938356 x 10-31 kgunless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb Coaxial cable -R1 High frequency signals are often transmitted along a coaxial cable, such as the one shown in the Figure. For example, the cable TV hookup coming into your home is a coaxial cable. A long coaxial cable carries a uniform (positive) surface charge density o1 = 6 µC/m?on the inner cylinder radius R1 = 0.2 mmand uniform surface charge density on the outer cylindrical shell (radius R2 = 1.7 mm The surface charge is negative and of just the right magnitude so that the cable as a whole is neutral.Use the following constants if necessary. Coulomb constant, k= 8.987 × 10° N. m² /C¥acuum permitivity, en = 8.854 x 10-12 F/ nMagnetic Permeability of vacuum, Ho = 12.566370614356 × 10-7 H/sMagnitude of the Charge of one electron, e= -1.60217662 × 10-19 CMass of one electron, m. = 9.10938356 x 10-31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µCmeans micro coulomb V2 I Ry P Vs R5 R { R7 You have given the above diagram of a resistor network. The numerical values of the resistors are R = 8 k, R2 = 8 M, R3 = 6 K R4 = 6 K, R5 = 4 kkQ R6 = 12 K) R = 4 KL And the e.m.f s are K = 10.0 volts V½ = 10.0 volts V½ = 10.0 volts a) Find the equivalent resistance across the terminal T'S. equivalent resistance Give your answer up to at least three significance digits. b)Draw the diagram in your script and then apply KVL and KCL to it. Write down the equations accordingly. ww
- d dompel mass pxing syatem , m= ao0sk=85N ohd b= 659/3. Calculte how bog it wiell take for its Cnesay to dsop one thisd of its ini tial Value? itUse the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m2 /Cvacuum permitivity, Eg = 8.854 x 10-12 F/rMagnetic Permeability of vacuum, Ho = 12.566370614356 x 10-7 H/aMagnitude of the Charge of one electron, e = -1.60217662 x 10-19 CMass of one electron, m. = 9.10938356 x 10-31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µCmeans micro coulomb In the figure the blue region represents a magnetic field B = 3.3 Tand the green region represents a magnetic field B2 = 6.0TA particle with charge 4.4 µG mass m =0.065 granand velocity v = 35 m/sravels toward the blue region as shown in the figure. a)What will be the shape of the path followed by the charge? Explain why this particular shape.Use the following constants if necessary. Coulomb constant, k = 8.987 × 10° N - m2 /CVacuum permitivity, eo = 8.854 × 10-12 F/nMagnetic Permeability of vacuum, µo = 12.566370614356 × 10-7 H/rMagnitude of the Charge of one electron, e = -1.60217662 × 10-19 CMass of one electron, me = 9.10938356 × 10 31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µCmeans micro coulomb The coordinate of the two charges q and q, are given by (16, 36) and (12, 31) These coordinates are in nano meters. x component of the position vector q1 Give your answer up to at least three significance digits. т y component of the position vector q1 Give your answer up to at least three significance digits. т x component of the position vector q2 Give your answer up to at least three significance digits. т y component of the position vector q2 Give your answer up to at least three significance digits. m