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Use Coulomb's law to determine the magnitude of the electric field at points A and B in the figure due to the two positive charges (Q = 7 \mu C, a = 5.4 cm) shown. Part A Express your answers using two significant figures separated by a comma. E_A,E_B = Part B Use Coulomb's law to determine the direction of the electric field at points A and B Express your answers using two significant figures separated by a comma. theta_A,theta_B = SOLUTION: One charge is placed at origin and the other charge is placed at (4a, 0). Electric field at a distance R is given by E Q 4 0 R 2 aR . Where Q is charge, R is the distance between charge Q and the point where filed is to be calculated aR is unit vector in the direction of line joining Q and the point. For positive charge, it points away from the charge. 0 is permittivity of space. 0 1 Farad / m 36 109 At point B, the field will be vector sum of the field created by charges at origin and at the point (4a,0). 2 5.4 3 For charge at origin and point B, R a a 2a 2 2 2.916 10 . 100 2 Unit vector aR ai aj 2a 2 i j . 2 2 2 2 2 5.4 3 10 2.916 10 100 Similarly, for charge at (4a,0) and point B, R 2 9a 2 a 2 10a 2 10 Unit vector aR Hence, EB = 3ai aj 10a 2 3i j . 10 7 106 4 1 36 109 i j 2 2.916 103 2 4 7 106 1 36 109 3i j 10 2.916 10 3 10 7.64 106 i 7.64 106 j 2.049 106 i 0.6832 106 j 5.591106 i 8.3232 106 j 10.026 106 56.1090 Similarly, at point A, EA = 7 106 4 1 36 109 2i j 3 5 4 5 2.916 10 1.932 106 (2i j ) 1.932 106 (2i j ) 3.864 106 j 3.864 106 900 Hence, part A EA 3.864 106 N / Coulomb EB 10.026 106 N / Coulomb Part B A 900 B 56.1090 7 106 1 36 109 2i j 5 5 2.916 103