#6. One the following vector fields F(x,y,z)= xyz*i +x²z*j+4x²yz³k G(x, y,z)=i+ (sin z) j + y (cos z) k is conservative and other is not. (a) Determine whether F is conservative or not. (b) Determine whether G is conservative or not. (c) For the vector field that is conservative find a function f such that the vector field is equal to Vf.
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A: Solution: a). The system of the three charges is shown in the figure below.
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- 3Four point charges have the same magnitude of 2.47 10-12 C and are fixed to the corners of a square that is 4.25 cm on a side. Three of the charges are positive and one is negative. Determine the magnitude of the net electric field that exists at the center of the square. N/Cpart A) A proton begins at the negative plate of a parallel plate capacitor. The plates are separated by 12 cm and generate a constant electric field of 3,283 N/C directed from the positive plate to the negative plate. The proton is "launched" with an initial velocity of 5 x 105 m/s at an angle of 30o from the horizontal. What is the maximum height that the proton achieves above the negative plate before falling back down? Express your answer in centimeters. part B) A particle with a charge of 4.4 μC and a mass of 0.00088 kg is fired horizontally with a speed of 4 x 103 m/s from an initial height of 0.04 meters above a negatively charged surface. The surface generates a constant electric field of 52,552 N/C. How far does the particle travel horizontally before striking the surface? Express your answer in meters. Please answer both parts A and B, I have been confused for an hour! Please help!!
- 8Three identical point charges (+52 µC) are placed at the corners of an equilateral triangle that has (20 cm sides. How much work ( in units of J) is required to assemble this charge arrangement starting with each of the charges a very large distance from any of the other charges? Select one: A. 270.4 B. 365.0 C. 216.3 D. 135.21) Calculate the voltage in a spherical conductor. You need to use the integral form of AV. O + The conductor is effectively a point charge from outside the conductor. This problem is far out. Start from infinity and come up to the surface of the conductor imagining there is a point charge in the middle of the conductor. Use this information to set a up and integral form for AV. Then solve. Then apply the fact that the V = const in a conductor
- 4. The electric field near a charged, long, narrow, wire (think of monofilament, fishing line) was hinted at in homework 01 by solving a source charge integration problem. The electric field to the side of a charged, narrow wire (or rod) of length 2a was found to be 1 xdy Q 2a 1 B = 47², (^) (2² +2² ²2² = 425, (204) (2√2² + 2² Απερ (1). 3/2 ATTE a 1 Απε simpler expression E = Q o(x√x² + a² Then, one can take the limit as the length a tends toward infinity to obtain the much 20₁ 2TE T r. Here, we have transitioned from a distance r to the side of the wire (in the x-y plane) to a more general, radial distance out from the wire in any plane (not just the z-y plane). This same simpler equation can be very easily obtained by applying Gauss' Law using an appropriate Gaussian surface that surrounds part of an infinitely long, charged wire. Find this derivation (in a book or online) and rewrite it below. Add verbal explanations to take the reader through the derivation, equation by equation.16. Divergence of the function D çâr in spherical polar coordinates is %3D 4ar2 (a) Zero (b) 1 (c) 2 (d) 3 17. The dimension of µo€, is (a) L-2T² (b) L²T-2 (c) L-²T-2 (d) L²T²A ▬ >E h d - As shown in the figure above, a positively charged ball is placed at point A and slides down the slope from rest. The area has a uniform electric field E = 12.9 N/C, pointing to the right. The mass of the ball is m = 9 kg and the charge is q = +2.6 C. When the ball reaches point B, it travels horizontally there after. The height from A to B is h = 37 m and the horizontal distance between A and B is d = 30 m. You can ignore friction and use g = 10 m/s for your calculation. %3D How much is the kinetic energy of the ball when it reaches at B (in the unit of J)? Submit Answer Tries 0/2 If the electric field ist changed to the opposite direction, How much is the kinetic energy of the ball when it reaches at B (in the unit of J) now? Submit Answer Tries 0/2 What is the minimum strength of electric field E that can be used to stop the particle right at Point B? N/C
- 73.1Part A Consider an initial system of three charges shown in (Figure 1). An object with charge q4 = + 8.0 × 10–8 C will be moved to position C from infinity (not shown in the figure). Part B qi = q2 = q3 = +10.0 × 10-8 C. Part C Part D -9 Determine the work done on the system by moving the charge q4 from infinity to point C, but for q1 = q3 = -10.0 × 10º C and q2 = +10.0 × 10 º C. Express your answer with the appropriate units, to two significant figures. HA ? Figure 1 of 1 W' = Value Units Submit Request Answer 20.0 cm Provide Feedback 92 20.0 cm C 20.0 cm 93