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2. Quadrupole potential Given a charge distribution p(7)= q8(f-ai)+qô(f+ai)- qô(f-a2) - qố (f+ā2), where q >...
OEM . . ., 2. A world with a quadrupole (20 pts.) (a) We have two...
OEM . . ., 2. A world with a quadrupole (20 pts.) (a) We have two positive point charges, + at two diagonal corners of a square (sta, ta, 0) and two minus charges - at the two other diagonals of a square (ta, Fa, 0). Using linear superposition, find the electric potential ( in a Taylor expansion, assuming 171a. What is the leading non-zero term? (b) Given the charges as specified in (a), evaluate explicitly the monopole, dipole, and...
2. Electric dipole (20%) A very common charge arrangement in electromagnetics is the dipole. A charge...
2. Electric dipole (20%) A very common charge arrangement in electromagnetics is the dipole. A charge dipole is illustrated in the figure below. In this problem, we will find the potential and field due to a dipole. tq X (a) Find the electrostatic potential at an arbitrary position in spherical coordinates, that is find the potential at the position (r, 0,0). (b) For large values of r, we can write: Z(17 cos 0 + -1/2 ~(1 7. cos 6)-1/2 ~...
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
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p....
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
0 For the charge distribution given above, each grid line represents 1 em and Q 2.10-4...
0 For the charge distribution given above, each grid line represents 1 em and Q 2.10-4 C. A negative test charge with q--5.10-5C and m- 1.2.10-6 kg is then placed at Point P and released. Make a model (system schema, energy bar charts, electric potential lines, description of the motion) and calculate the speed of the test charge when it is 0.1 cm away from the positive charge.
Only Need F and G m l Two small insulating balls with charge +q and mass...
Only Need F and G
m l Two small insulating balls with charge +q and mass m are placed in a circular bowl with radius R as shown above and are free to move without friction. You may assume that the radius of the balls is negligible compared to the radius of the bowl a) If we begin with the balls at the top of the bowl (i.e. -90°), what is the total gravitational potential energy of both balls? You...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make...
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make sure you derive expressions for the cdf in the regions • x < 0 or y < 0; • 0 ≤ x ≤ 1, 0 ≤ y ≤ 1; • x > 1, 0 ≤ y ≤...
OEM . . ., 2. A world with a quadrupole (20 pts.) (a) We have two positive point charges, + at two diagonal corners of a square (sta, ta, 0) and two minus charges - at the two other diagonals of a square (ta, Fa, 0). Using linear superposition, find the electric potential ( in a Taylor expansion, assuming 171a. What is the leading non-zero term? (b) Given the charges as specified in (a), evaluate explicitly the monopole, dipole, and...
2. Electric dipole (20%) A very common charge arrangement in electromagnetics is the dipole. A charge dipole is illustrated in the figure below. In this problem, we will find the potential and field due to a dipole. tq X (a) Find the electrostatic potential at an arbitrary position in spherical coordinates, that is find the potential at the position (r, 0,0). (b) For large values of r, we can write: Z(17 cos 0 + -1/2 ~(1 7. cos 6)-1/2 ~...
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
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
0 For the charge distribution given above, each grid line represents 1 em and Q 2.10-4 C. A negative test charge with q--5.10-5C and m- 1.2.10-6 kg is then placed at Point P and released. Make a model (system schema, energy bar charts, electric potential lines, description of the motion) and calculate the speed of the test charge when it is 0.1 cm away from the positive charge.
Only Need F and G
m l Two small insulating balls with charge +q and mass m are placed in a circular bowl with radius R as shown above and are free to move without friction. You may assume that the radius of the balls is negligible compared to the radius of the bowl a) If we begin with the balls at the top of the bowl (i.e. -90°), what is the total gravitational potential energy of both balls? You...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
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