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. (5 Points) Consider a quadrupole with charges +q(t) = go cos(wt) at positions ±d/ and...
3, (10 Points) Show that the vector potential A for the quadrupole arrangement is cos e wtol Hint...
3, (10 Points) Show that the vector potential A for the quadrupole arrangement is cos e wtol Hint: last week we already calculated Griffiths Eq. 11.16 to second order for a dipole. Again, you can use problem 1 to simplify the 1/R terms. Again, you only need teo expand the numerator to first order . (5 Extra Credit Points) You now have A and V. Calculate E and B. 1. (5 Points) In the previous homework, I claimed that the...
electric field and flux 1.16 Gauss's law and two point charges* (a) Two point charges q...
electric field and flux
1.16 Gauss's law and two point charges* (a) Two point charges q are located at positions x = ±1. At points close to the origin on the x axis, find Ex. At points close to the origin on the y axis, find Ey. Make suitable approximations with x <E and y< e (b) Consider a small cylinder centered at the origin, with its axis along the x axis. The radius is ro and the length is...
2. Three charges are fixed at positions along the a-axis as positions -d, o, and +d....
2. Three charges are fixed at positions along the a-axis as positions -d, o, and +d. The charges at -d and d are both and the charge at O is positive. (a) A positively charged object of mass m is placed on the x-axis between O and d, close to the positlicn the three charges described above do not move as a result of this new charged object, describe the mois object after it is released as it moves in...
1. Antenna problem A wire of length L has its center at the origin, and lies along the z axis. The current carried by the wire is of the form I(,)-locos(wt) cos(1). Consider positions in the radiatio...
1. Antenna problem A wire of length L has its center at the origin, and lies along the z axis. The current carried by the wire is of the form I(,)-locos(wt) cos(1). Consider positions in the radiation zone. (a) Compute A(r, t) b) Compute E(r,t) and B(r, t) (c) Compute the angular distribution of radiated power
1. Antenna problem A wire of length L has its center at the origin, and lies along the z axis. The current carried by...
a) In the picture below, the 3 charges Q1, Q2 and Q3 are located at positions...
a) In the picture below, the 3
charges Q1, Q2 and Q3 are located at positions (-a,0), (a,0) and
(0,-d) respectively. (The origin is the point halfway between Q1
and Q2.) Consider the special case where Q1, Q3 greater than zero
and Q2 = -Q1. Select true or false for each statement. The force on
Q3 due to the other two charges is zero. The electric potential at
any point along the y-axis is positive. If Q3 is released from...
Please answer question 1, a-d Bo cos(wt) 2 (T). o points) A time-varying magnetic flux density...
Please answer question 1, a-d
Bo cos(wt) 2 (T). o points) A time-varying magnetic flux density in space is given by B A closed rectangle loop with sides a and b is centered at the origin and lies in the r-y plane. Solve steps a)-e) to find the induced emf a) (1o points) Draw a sketch in Cartesian coordinates. Show the loop and magnetic flux density b) (5 points) List the appropriate Maxwell equation to solve this problem c) (5...
Q1. MULTIPOLES - point charges You haye four point charges. Their location and charges in Cartesian...
Q1. MULTIPOLES - point charges You haye four point charges. Their location and charges in Cartesian coordinates are: A positive charge -2q located at (a,0,0), another charge -2q located at (-2,0,0), a 3rd charge -q located at (0,0,b), and finally a fourth charge +57 located at (0,0,-b) - What is the total charge, and dipole moment, of this distribution of charges? Use the methods of "the multipole expansion" (Griffiths section 3.4.1) to find a simple approximate formula for V(r,0) (in...
2. (8 pts) Consider the screened Coulomb potential of a point charge q that arises e.g....
2. (8 pts) Consider the screened Coulomb potential of a point charge q that arises e.g. in plasma physics: V(r) = kq xPL T/A), where is a constant called screening length. a) (2 pts) Determine E(r) associated with potential. b) (2 pts) Find the charge distribution p(r) that produces this potential. (Think carefully about what happens at the origin!) c) (2 pts) Show by explicit integration over p(r) that the charge represented by this distribution is zero. (If you don't...
You have four point charges. Their location and charges in Cartesian coordinates are: a positive charge,...
You have four point charges. Their location and charges in Cartesian coordinates are: a positive charge, 2q, located at (a,0,0), another charge -2q located at (-a,0,0), a 3rd charge -q located at (0,0,b), and finally a fourth charge +5q located at (0,0,-b) (a) What is the total charge, and dipole moment, of this distribution of charges? Use the methods of "the multipole expansion" (Griffiths section 3.4.1) to find a simple approximate formula for V(r,0) (in spherical coordinates!) valid at points...
Consider the following figure. +24 For the arrangement of charges in the figure, calculate the electric...
Consider the following figure. +24 For the arrangement of charges in the figure, calculate the electric potential (in v) at point P. Use q-9.0 nc and d 5.4 m, and assume that v- 0 v at infinite distance. (a) 114 (b) If a charge -2q is brought to point P, what is the electric energy of this charge (in V)? Assume again that the electric potential energy is zero at infinite distance
3, (10 Points) Show that the vector potential A for the quadrupole arrangement is cos e wtol Hint: last week we already calculated Griffiths Eq. 11.16 to second order for a dipole. Again, you can use problem 1 to simplify the 1/R terms. Again, you only need teo expand the numerator to first order . (5 Extra Credit Points) You now have A and V. Calculate E and B. 1. (5 Points) In the previous homework, I claimed that the...
electric field and flux
1.16 Gauss's law and two point charges* (a) Two point charges q are located at positions x = ±1. At points close to the origin on the x axis, find Ex. At points close to the origin on the y axis, find Ey. Make suitable approximations with x <E and y< e (b) Consider a small cylinder centered at the origin, with its axis along the x axis. The radius is ro and the length is...
2. Three charges are fixed at positions along the a-axis as positions -d, o, and +d. The charges at -d and d are both and the charge at O is positive. (a) A positively charged object of mass m is placed on the x-axis between O and d, close to the positlicn the three charges described above do not move as a result of this new charged object, describe the mois object after it is released as it moves in...
1. Antenna problem A wire of length L has its center at the origin, and lies along the z axis. The current carried by the wire is of the form I(,)-locos(wt) cos(1). Consider positions in the radiation zone. (a) Compute A(r, t) b) Compute E(r,t) and B(r, t) (c) Compute the angular distribution of radiated power
1. Antenna problem A wire of length L has its center at the origin, and lies along the z axis. The current carried by...
a) In the picture below, the 3
charges Q1, Q2 and Q3 are located at positions (-a,0), (a,0) and
(0,-d) respectively. (The origin is the point halfway between Q1
and Q2.) Consider the special case where Q1, Q3 greater than zero
and Q2 = -Q1. Select true or false for each statement. The force on
Q3 due to the other two charges is zero. The electric potential at
any point along the y-axis is positive. If Q3 is released from...
Please answer question 1, a-d
Bo cos(wt) 2 (T). o points) A time-varying magnetic flux density in space is given by B A closed rectangle loop with sides a and b is centered at the origin and lies in the r-y plane. Solve steps a)-e) to find the induced emf a) (1o points) Draw a sketch in Cartesian coordinates. Show the loop and magnetic flux density b) (5 points) List the appropriate Maxwell equation to solve this problem c) (5...
Q1. MULTIPOLES - point charges You haye four point charges. Their location and charges in Cartesian coordinates are: A positive charge -2q located at (a,0,0), another charge -2q located at (-2,0,0), a 3rd charge -q located at (0,0,b), and finally a fourth charge +57 located at (0,0,-b) - What is the total charge, and dipole moment, of this distribution of charges? Use the methods of "the multipole expansion" (Griffiths section 3.4.1) to find a simple approximate formula for V(r,0) (in...
2. (8 pts) Consider the screened Coulomb potential of a point charge q that arises e.g. in plasma physics: V(r) = kq xPL T/A), where is a constant called screening length. a) (2 pts) Determine E(r) associated with potential. b) (2 pts) Find the charge distribution p(r) that produces this potential. (Think carefully about what happens at the origin!) c) (2 pts) Show by explicit integration over p(r) that the charge represented by this distribution is zero. (If you don't...
You have four point charges. Their location and charges in Cartesian coordinates are: a positive charge, 2q, located at (a,0,0), another charge -2q located at (-a,0,0), a 3rd charge -q located at (0,0,b), and finally a fourth charge +5q located at (0,0,-b) (a) What is the total charge, and dipole moment, of this distribution of charges? Use the methods of "the multipole expansion" (Griffiths section 3.4.1) to find a simple approximate formula for V(r,0) (in spherical coordinates!) valid at points...
Consider the following figure. +24 For the arrangement of charges in the figure, calculate the electric potential (in v) at point P. Use q-9.0 nc and d 5.4 m, and assume that v- 0 v at infinite distance. (a) 114 (b) If a charge -2q is brought to point P, what is the electric energy of this charge (in V)? Assume again that the electric potential energy is zero at infinite distance
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