2 Consider a square of side length b whose two diagonals lie on the x-axis and y-axis of our coordinate system. Two negative charges Q₁ = Q3 = √√24 are located in the top and bottom corner of the square (locations 1 and 3 in the schematic), whereas a positive charge Q2 +2q is located in the left corner of the square (location 2 in the schematic). In the center of the square +2q (origin), there is a small neutral particle with polarizability a. y -√29.1 b 4 x b √2 -√29 3 1. [8pts] Determine the electric field E123 in the right corner of the square (position 4 in the schematic) that is due to the combined effect of the charges Q1, Q2, and Q3. 2. [4pts] Determine the net external field E123 at the location of the polar- izable particle. -√√29.1 b 2 4 X +2q b √2 -√29 3 3. [8pts] Determine (i) the induced electric dipole moment of the polarizable particle, and (ii) the ensuing electric field Ea in location 4.

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Consider a square of side length b whose two diagonals lie on
the x-axis and y-axis of our coordinate system. Two negative
charges Q₁ = Q3 = √√24 are located in the top and bottom
corner of the square (locations 1 and 3 in the schematic), whereas
a positive charge Q2 +2q is located in the left corner of the
square (location 2 in the schematic). In the center of the square +2q
(origin), there is a small neutral particle with polarizability a.
y
-√29.1
b
4
x
b
√2
-√29 3
1. [8pts] Determine the electric field E123 in the right corner of the square (position 4 in the schematic) that is
due to the combined effect of the charges Q1, Q2, and Q3.
Transcribed Image Text:2 Consider a square of side length b whose two diagonals lie on the x-axis and y-axis of our coordinate system. Two negative charges Q₁ = Q3 = √√24 are located in the top and bottom corner of the square (locations 1 and 3 in the schematic), whereas a positive charge Q2 +2q is located in the left corner of the square (location 2 in the schematic). In the center of the square +2q (origin), there is a small neutral particle with polarizability a. y -√29.1 b 4 x b √2 -√29 3 1. [8pts] Determine the electric field E123 in the right corner of the square (position 4 in the schematic) that is due to the combined effect of the charges Q1, Q2, and Q3.
2. [4pts]
Determine the net external field E123 at the location of the polar-
izable particle.
-√√29.1
b
2
4
X
+2q
b
√2
-√29 3
3. [8pts] Determine
(i) the induced electric dipole moment of the polarizable particle, and
(ii) the ensuing electric field Ea in location 4.
Transcribed Image Text:2. [4pts] Determine the net external field E123 at the location of the polar- izable particle. -√√29.1 b 2 4 X +2q b √2 -√29 3 3. [8pts] Determine (i) the induced electric dipole moment of the polarizable particle, and (ii) the ensuing electric field Ea in location 4.
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