Superposition Electric Field From a Dipole Superposition and Dipole E~ field PHYS 272 - David Blasing Tuesday June 11th 1 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Principle of Superposition Definition: Superposition The net electric field at a position in space is the vector sum of every electric field made at that location by all the other charged particles around. The electric field created by a charged particle is not affected by the presence of other charged particles or electric fields nearby. 2 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Superposition Example 3 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere ~ ~ Enet is related to Fnet Once you have calculated the E~net due to all the other charges, then you can quickly calculate the force F~net = Q ∗ E~net on any amount of charge Q placed at that location 4 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Clicker Question 1 What is the direction of E~net at the location of q3 if jq2j ≈ 2jq1j ? 5 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Clicker Question 1 What is the direction of E~net at the location of q3? 6 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Clicker Question 2 7 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Clicker Question 3 8 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Clicker Question 4 9 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Clicker Question 5 10 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere Electric field of a uniformly charged sphere for r > R ~ 1 Q Esphere = 2 r^ 4π0 r for r < R ~ Esphere = 0 11 / 30 2 A uniformly charged sphere at locations outside the sphere produces the same E~ field of a point charge with charge equal to the total charge on the sphere. The charged sphere responds to applied electric fields in the same way as a point charge at its center would Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere E~ from a Uniformly Charged Sphere 1 ~ 1 Q Note: for r > R, E = 2 r^. Does this formula look sphere 4π0 r familiar? 12 / 30 Definition Superposition Clicker Question Electric Field From a Dipole E~ from a Uniformly Charged Sphere E~ from a Uniformly Charged Sphere 1 ~ 1 Q Note: for r > R, E = 2 r^. Does this formula look sphere 4π0 r familiar? 2 A uniformly charged sphere at locations outside the sphere produces the same E~ field of a point charge with charge equal to the total charge on the sphere. The charged sphere responds to applied electric fields in the same way as a point charge at its center would 12 / 30 Definition: Dipole Moment Vector p~ p~ = q~s where q is the magnitude of both charges that make up a dipole, ~s is the position of the positive charge relative to the negative charge. Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary E~ field of a dipole and the electric dipole moment vector 13 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary E~ field of a dipole and the electric dipole moment vector Definition: Dipole Moment Vector p~ p~ = q~s where q is the magnitude of both charges that make up a dipole, ~s is the position of the positive charge relative to the negative charge. 13 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary E~ field of a dipole at other locations Part of one of your labs will recreate this plot. 14 / 30 3 There are two lines of symmetry for a dipole, and we are going to derive simpler formulas along each of those lines. Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Parallel to the Axis 1 Now we are going to apply the principal of superposition to get the electric field of a dipole. 2 As a general hint, symmetry is your friend. Doing math is usually simpler when you somehow preserve or take advantage of a physical symmetry. 15 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Parallel to the Axis 1 Now we are going to apply the principal of superposition to get the electric field of a dipole. 2 As a general hint, symmetry is your friend. Doing math is usually simpler when you somehow preserve or take advantage of a physical symmetry. 3 There are two lines of symmetry for a dipole, and we are going to derive simpler formulas along each of those lines. 15 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Parallel to the Axis 16 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Parallel to the Axis 17 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Parallel to the Axis 18 / 30 1 While the electric field of a point charge is proportional to r 2 , electric fields created by several charges may have a different distance dependence. Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Parallel to the Axis 19 / 30 1 While the electric field of a point charge is proportional to r 2 , electric fields created by several charges may have a different distance dependence. Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Parallel to the Axis 19 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Parallel to the Axis 1 While the electric field of a point charge is proportional to r 2 , electric fields created by several charges may have a different distance dependence. 19 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 20 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 21 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 22 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 23 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 24 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 25 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 26 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 27 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Summary Dipole E~ Field E~ Far From the Dipole ~ 1 p ~ 1 2p jEperpj = 3 jEonaxis j = 3 4π0 y 4π0 r ~ ~ For the same distance r, jEonaxis j = 2 ∗ jEperpj. At other locations you can still use superposition, it is just that the formula doesn't simplify as nicely. 28 / 30 The force on the positive is equal in magnitude but opposite in direction of the force on the negative, so F~net = F~+ + F~− = ~0 So what could a dipole be used to measure? A dipole would experience a force in a non-uniform E~ field. So they can measure the uniformity of the E~ field Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Group Question 1 Dipole in a uniform E~ field, What is the net force? 29 / 30 So what could a dipole be used to measure? A dipole would experience a force in a non-uniform E~ field. So they can measure the uniformity of the E~ field Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Group Question 1 Dipole in a uniform E~ field, What is the net force? The force on the positive is equal in magnitude but opposite in direction of the force on the negative, so F~net = F~+ + F~− = ~0 29 / 30 A dipole would experience a force in a non-uniform E~ field. So they can measure the uniformity of the E~ field Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Group Question 1 Dipole in a uniform E~ field, What is the net force? The force on the positive is equal in magnitude but opposite in direction of the force on the negative, so F~net = F~+ + F~− = ~0 So what could a dipole be used to measure? 29 / 30 Electric Dipoles Superposition Parallel to the Axis Electric Field From a Dipole Perpendicular to the Axis Dipole Summary Group Question 1 Dipole in a uniform E~ field, What is the net force? The force on the positive is equal in magnitude but opposite in direction of the force on the negative, so F~net = F~+ + F~− = ~0 So what could a dipole be used to measure? A dipole would experience a force in a non-uniform E~ field.