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8. The charge distribution of a quadrupole is as shown below. (a) Show that the potential...
ferred to as a linear quadrupole. (a) Find the exact expression for the potential at a...
ferred to as a linear quadrupole. (a) Find the exact expression for the potential at a point on the x axis where x > d. (b) Show that the expression obtained in Use the exact result from Problem 8.to evaluate the potential for the linear quadrupole at x-3d if d- 2 mm and 9-3 μ。. Compare this answer to what you obtain when f when z d nd you use theare thi ˇ-의 2kOd when x > d 2Q +...
2. Quadrupole potential Given a charge distribution p(7)= q8(f-ai)+qô(f+ai)- qô(f-a2) - qố (f+ā2), where q >...
2. Quadrupole potential Given a charge distribution p(7)= q8(f-ai)+qô(f+ai)- qô(f-a2) - qố (f+ā2), where q > 0 and ai and a2 given in Cartesian coordinates by ai = (a,0,0) and ā2 = (0, a,0) with a > 0. are a) Calculate the resulting potential p and the electric field b) What is the electrostatic energy of the charge distribution (without the self-energy contri- bution of the point charges themselves)? c) Determine the dipole moment p= f d*r'rp(F) and the quadrupole...
Quadrupole charge distribution. Consider the four-charge distribution in the xy- plane along the x-axis, the y-axis,...
Quadrupole charge distribution. Consider the four-charge distribution in the xy- plane along the x-axis, the y-axis, and in the x = y direction for positive charges at a (1,1), a (-1,-1) and negative charges at a (11) and a (-1,1). Take the absolute value of the charges to be the same and equal to q. a) Recall in class we found that for the dipole charge distribution there are two axes of symmetry defined to be straight lines to which...
8) We can construct a quadrupole from two dipoles as shown in the picture below. What...
8) We can construct a quadrupole from two dipoles as shown in the picture below. What is the exact direction of the electric field on the positive x axis (far from quadrupole)? on the negative x-axis (far from quadrupole)? on the positive y-axis (far from quadrupole)?
Two point charges are located as shown below. One has charge +40 and located at (x,...
Two point charges are located as shown below. One has charge +40 and located at (x, y)-(-a, 0). The other has charge-Q and located at (ta, 0). a) b) c) Find the potential Vat (x, y) (0, 0). (Assume V- 0 at infinitely-far-way places.) Find the potential V at point P-(0, +a). Find out the location (x, 0) where the potential V becomes zero in the x-axis. There is such a point other than infinitely-far-way places d) What is the...
A charge distribution is given as shown below. What is the total potential at point P?...
A charge distribution is given as shown below. What is the total potential at point P? What is the electric field? 7. 6+4 points P(x.y) Y>R Radius R
6. Consider a thin rod of length L laying on the x-axis as shown in the...
6. Consider a thin rod of length L laying on the x-axis as shown in the figure below. The charge density is nonuniform and varies as λ-λ, x/L, where λ° is a constant. (a) Find the magnitude of the force on a point charge q at x = a in terms of q, , a, and L. (b) Show that for a >> L the answer in (a) reduces to c) What is the total charge on the rod? (d)...
Continuous charge distribution (finding V from the point-charge formula V = S kdq/r). A uniformly charged...
Continuous charge distribution (finding V from the point-charge formula V = S kdq/r). A uniformly charged rod lies along the y-axis with its center at origin. It has a total charge Q and length L. (a) Find an expression for V(x) as a function of x. (b) Show that your answer in part (a) reduces to the expected form when x > L. (Hint: For part (b) you can use two extremely useful formulas, called Taylor series approximations. These tell...
1. A distribution of positive charge creates an E-field that fills the space around the distribution...
1. A distribution of positive charge creates an E-field that fills the space around the distribution such that the the electric potential at x = 10 m has a bigger magnitude than at x = 20 m. Assume that the charge causing the field is all to the left of x = 0. Given this information, which of the following is not possible? (A). The E-field at x = 10 m is directed along the +x axis. (B). The E-field...
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...
ferred to as a linear quadrupole. (a) Find the exact expression for the potential at a point on the x axis where x > d. (b) Show that the expression obtained in Use the exact result from Problem 8.to evaluate the potential for the linear quadrupole at x-3d if d- 2 mm and 9-3 μ。. Compare this answer to what you obtain when f when z d nd you use theare thi ˇ-의 2kOd when x > d 2Q +...
2. Quadrupole potential Given a charge distribution p(7)= q8(f-ai)+qô(f+ai)- qô(f-a2) - qố (f+ā2), where q > 0 and ai and a2 given in Cartesian coordinates by ai = (a,0,0) and ā2 = (0, a,0) with a > 0. are a) Calculate the resulting potential p and the electric field b) What is the electrostatic energy of the charge distribution (without the self-energy contri- bution of the point charges themselves)? c) Determine the dipole moment p= f d*r'rp(F) and the quadrupole...
Quadrupole charge distribution. Consider the four-charge distribution in the xy- plane along the x-axis, the y-axis, and in the x = y direction for positive charges at a (1,1), a (-1,-1) and negative charges at a (11) and a (-1,1). Take the absolute value of the charges to be the same and equal to q. a) Recall in class we found that for the dipole charge distribution there are two axes of symmetry defined to be straight lines to which...
8) We can construct a quadrupole from two dipoles as shown in the picture below. What is the exact direction of the electric field on the positive x axis (far from quadrupole)? on the negative x-axis (far from quadrupole)? on the positive y-axis (far from quadrupole)?
Two point charges are located as shown below. One has charge +40 and located at (x, y)-(-a, 0). The other has charge-Q and located at (ta, 0). a) b) c) Find the potential Vat (x, y) (0, 0). (Assume V- 0 at infinitely-far-way places.) Find the potential V at point P-(0, +a). Find out the location (x, 0) where the potential V becomes zero in the x-axis. There is such a point other than infinitely-far-way places d) What is the...
A charge distribution is given as shown below. What is the total potential at point P? What is the electric field? 7. 6+4 points P(x.y) Y>R Radius R
6. Consider a thin rod of length L laying on the x-axis as shown in the figure below. The charge density is nonuniform and varies as λ-λ, x/L, where λ° is a constant. (a) Find the magnitude of the force on a point charge q at x = a in terms of q, , a, and L. (b) Show that for a >> L the answer in (a) reduces to c) What is the total charge on the rod? (d)...
Continuous charge distribution (finding V from the point-charge formula V = S kdq/r). A uniformly charged rod lies along the y-axis with its center at origin. It has a total charge Q and length L. (a) Find an expression for V(x) as a function of x. (b) Show that your answer in part (a) reduces to the expected form when x > L. (Hint: For part (b) you can use two extremely useful formulas, called Taylor series approximations. These tell...
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...
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