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2. In lecture we saw (or will see) that very far away from an electric dipole the electric field is proportional to 1/³ where r is the distance away from the center of the dipole. Below is an electric quadruple: two negative point charges -q a distance d from a positive point charge 2q. d +2q d T -q OP a) As done for the dipole, consider the electric field along the quadruple axis (at the point P). Find an expression for the electric field in the far field limit r >> d, where r is the distance from the center of the quadruple, as shown above. In particular, expand the electric field in appropriate powers of r and determine the highest power of r. b) Suppose the charge in the middle is 3q instead of 2q. What would you expect for the highest power of r in this case? You don't need to calculate it, just explain physically.

2. In lecture we saw (or will see) that very far away from an electric dipole the electric field is proportional to 1/³ where r is the distance away from the center of the dipole. Below is an electric quadruple: two negative point charges -q a distance d from a positive point charge 2q. d +2q d T -q OP a) As done for the dipole, consider the electric field along the quadruple axis (at the point P). Find an expression for the electric field in the far field limit r >> d, where r is the distance from the center of the quadruple, as shown above. In particular, expand the electric field in appropriate powers of r and determine the highest power of r. b) Suppose the charge in the middle is 3q instead of 2q. What would you expect for the highest power of r in this case? You don't need to calculate it, just explain physically.

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2. In lecture we saw (or will see) that very far away from an electric dipole the electric field is proportional to 1/r³ where r is the distance away from the center of the dipole. Below is an electric quadruple: two negative point charges -q a distance d from a positive point charge 2q. -9 (+2q) r P a) As done for the dipole, consider the electric field along the quadruple axis (at the point P). Find an expression for the electric field in the far field limit r >> d, where r is the distance from the center of the quadruple, as shown above. In particular, expand the electric field in appropriate powers of r and determine the highest power of r. b) Suppose the charge in the middle is 3q instead of 2q. What would you expect for the highest power of r in this case? You don't need to calculate it, just explain physically.
Transcribed Image Text:2. In lecture we saw (or will see) that very far away from an electric dipole the electric field is proportional to 1/r³ where r is the distance away from the center of the dipole. Below is an electric quadruple: two negative point charges -q a distance d from a positive point charge 2q. -9 (+2q) r P a) As done for the dipole, consider the electric field along the quadruple axis (at the point P). Find an expression for the electric field in the far field limit r >> d, where r is the distance from the center of the quadruple, as shown above. In particular, expand the electric field in appropriate powers of r and determine the highest power of r. b) Suppose the charge in the middle is 3q instead of 2q. What would you expect for the highest power of r in this case? You don't need to calculate it, just explain physically.
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