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Transcript
Superposition Electric Field From a Dipole Superposition and Dipole E~ field PHYS 272 - David Blasing Tuesday June 11th 1 / 30 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E 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 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E Superposition Example 3 / 30 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E E~net is related to F~net 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 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E Clicker Question 1 What is the direction of E~net at the location of q3 if |q2 | ≈ 2|q1 | ? 5 / 30 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E Clicker Question 1 What is the direction of E~net at the location of q3 ? 6 / 30 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E Clicker Question 2 7 / 30 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E Clicker Question 3 8 / 30 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E Clicker Question 4 9 / 30 Superposition Electric Field From a Dipole Definition Clicker Question ~ from a Uniformly Charged Sphere E Clicker Question 5 10 / 30 Definition Clicker Question ~ from a Uniformly Charged Sphere E Superposition Electric Field From a Dipole Electric field of a uniformly charged sphere for r > R E~sphere = 1 Q rˆ 4π0 r 2 for r < R E~sphere = 0 11 / 30 Definition Clicker Question ~ from a Uniformly Charged Sphere E Superposition Electric Field From a Dipole E~ from a Uniformly Charged Sphere 1 Note: for r > R, E~sphere = familiar? 1 Q 4π0 r 2 rˆ. Does this formula look 12 / 30 Definition Clicker Question ~ from a Uniformly Charged Sphere E Superposition Electric Field From a Dipole E~ from a Uniformly Charged Sphere 1 2 Note: for r > R, E~sphere = familiar? 1 Q 4π0 r 2 rˆ. Does this formula look 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 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary E~ field of a dipole and the electric dipole moment vector 13 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis 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 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis 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 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis 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 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis 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 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Parallel to the Axis 16 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Parallel to the Axis 17 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Parallel to the Axis 18 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Parallel to the Axis 19 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Parallel to the Axis 19 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Parallel to the Axis While the electric field of a point charge is proportional to r12 , electric fields created by several charges may have a different distance dependence. 19 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 20 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 21 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 22 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 23 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 24 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 25 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 26 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Perpendicular to the Axis 27 / 30 Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Superposition Electric Field From a Dipole Summary Dipole E~ Field E~ Far From the Dipole |E~perp | = 1 p 4π0 y 3 |E~onaxis | = 1 2p 4π0 r 3 For the same distance r , |E~onaxis | = 2 ∗ |E~perp |. At other locations you can still use superposition, it is just that the formula doesn’t simplify as nicely. 28 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Group Question 1 Dipole in a uniform E~ field, What is the net force? 29 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis 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 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis 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 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis 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. So they can measure the uniformity of the E~ field 29 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Group Question 2 Dipole in a uniform E~ field The E~ field results in a torque on the dipole, aligning p~ to E~ . Given this, what additional piece of information might a dipole measure? 30 / 30 Superposition Electric Field From a Dipole Electric Dipoles Parallel to the Axis Perpendicular to the Axis Dipole Summary Group Question 2 Dipole in a uniform E~ field The E~ field results in a torque on the dipole, aligning p~ to E~ . Given this, what additional piece of information might a dipole measure? The direction of E~ (i.e. Ê ) 30 / 30
