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5) An electric field is described by the following equation:E = s cos p sinp p...
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1)...
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1) to B(0,3) depicted in Figure 1 Figure 1. Rectangular path of the particle. Compute the work done by the force in this field; Using line integral (if the integral is difficult to evaluate, then use Matlab) b. Also using Green's Theorem without computer aid. Compare your results. a.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the...
4. Stoke's Theorem: Consider a vector field F = (1,1)+(1,0) + (0,0). tyle +rin the unit...
4. Stoke's Theorem: Consider a vector field F = (1,1)+(1,0) + (0,0). tyle +rin the unit square bordered by (0,0) + (0,1) ► (a) What is the curl of the vector field F? [2 points) (b) What is the path integral of the vector field around the unit square? [5 points) (c) Show your answers to the previous parts are consistent with Stoke's Theorem. HINT: consider the right-hand rule. (3 points]
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy,...
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
What is the electric potential at point P? What is the magnitude of the electric field...
What is the electric potential at point P?
What is the magnitude of the electric field at point P?
Q ...................s+20 Q 0 5. What is the electric potential at point P? (A) Zero (C) 4k01r (D) 5kgir 6. What is the magnitude of the electric field at point (A) Zero (B) ke/r (c) 2ke/r2
Locations A, B. and c are in a regon of uniform electric field, as shown n...
Locations A, B. and c are in a regon of uniform electric field, as shown n te diagram above. Location A is at <-03, o, o> m. Locaton cs atく0.4 electric field 1 . <-650, 350, o> NC. 0.3, 0M·In he region the For a path starting at C and endng at A, calculate: (a) The displacement vector Δ a7- (b) the change in electric potential: (e) the potential energy change for the system when a proton moves from c...
An electric field is described in cylindrical coordinates as Find the voltage drop VAB where d...
An electric field is described in cylindrical coordinates as Find the voltage drop VAB where d is the point (1, 0, 0) and B is the point (2, π/2, l). (In the description of these points, the cylindrical coordinate notation (p, p, z) is used, where dimensions are in [m] and angles are in radians.) Assume that the voltage drop is path independent (i.e., this is a valid electrostatic field), so you can use any path that you wish. Hint:...
Page #4 Physics Il caline lab: Electric Field & Elecric Potential Part I: Electric Field Open...
Page #4 Physics Il caline lab: Electric Field & Elecric Potential Part I: Electric Field Open the PHET simulation "Charges and Fields". Add positive and negative charges as shown in the diagram below. Draw appropriate electric field lines around and in between the two charges. Use the tools available in the software and then draw manually. Where is the electric field the largest? (label the point #1 in your diagram) 2. Where is the electric field equal to zero? (label...
8. (5 points) Two charges are placed as shown in the diagram. If the electric field...
8. (5 points) Two charges are placed as shown in the diagram. If the electric field at point P has no y-component, what must be the charge on A? (magnitude and sign) P 60° 30° A +2C 9. (1 point) In problem 8, which direction does the electric field point at point P?
Find E_y the y-component of the total electric field at P. Find the magnitude and direction...
Find E_y the y-component of the total electric field at P. Find the magnitude and direction of the total electric field at P Find the total electrical potential energy between the 5 nC and 7 nC charges Take a point charge + 5 nC at x = -1 and point charge +7 nC at x = 2 Now there is a point charge + 4 nC on the y-axis at y = 3: Find the length of the distance r_1...
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1) to B(0,3) depicted in Figure 1 Figure 1. Rectangular path of the particle. Compute the work done by the force in this field; Using line integral (if the integral is difficult to evaluate, then use Matlab) b. Also using Green's Theorem without computer aid. Compare your results. a.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the...
4. Stoke's Theorem: Consider a vector field F = (1,1)+(1,0) + (0,0). tyle +rin the unit square bordered by (0,0) + (0,1) ► (a) What is the curl of the vector field F? [2 points) (b) What is the path integral of the vector field around the unit square? [5 points) (c) Show your answers to the previous parts are consistent with Stoke's Theorem. HINT: consider the right-hand rule. (3 points]
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
What is the electric potential at point P?
What is the magnitude of the electric field at point P?
Q ...................s+20 Q 0 5. What is the electric potential at point P? (A) Zero (C) 4k01r (D) 5kgir 6. What is the magnitude of the electric field at point (A) Zero (B) ke/r (c) 2ke/r2
Locations A, B. and c are in a regon of uniform electric field, as shown n te diagram above. Location A is at <-03, o, o> m. Locaton cs atく0.4 electric field 1 . <-650, 350, o> NC. 0.3, 0M·In he region the For a path starting at C and endng at A, calculate: (a) The displacement vector Δ a7- (b) the change in electric potential: (e) the potential energy change for the system when a proton moves from c...
An electric field is described in cylindrical coordinates as Find the voltage drop VAB where d is the point (1, 0, 0) and B is the point (2, π/2, l). (In the description of these points, the cylindrical coordinate notation (p, p, z) is used, where dimensions are in [m] and angles are in radians.) Assume that the voltage drop is path independent (i.e., this is a valid electrostatic field), so you can use any path that you wish. Hint:...
Page #4 Physics Il caline lab: Electric Field & Elecric Potential Part I: Electric Field Open the PHET simulation "Charges and Fields". Add positive and negative charges as shown in the diagram below. Draw appropriate electric field lines around and in between the two charges. Use the tools available in the software and then draw manually. Where is the electric field the largest? (label the point #1 in your diagram) 2. Where is the electric field equal to zero? (label...
8. (5 points) Two charges are placed as shown in the diagram. If the electric field at point P has no y-component, what must be the charge on A? (magnitude and sign) P 60° 30° A +2C 9. (1 point) In problem 8, which direction does the electric field point at point P?
Find E_y the y-component of the total electric field at P. Find the magnitude and direction of the total electric field at P Find the total electrical potential energy between the 5 nC and 7 nC charges Take a point charge + 5 nC at x = -1 and point charge +7 nC at x = 2 Now there is a point charge + 4 nC on the y-axis at y = 3: Find the length of the distance r_1...
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