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Chapter 21 Electric Charge and Electric Field

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Charles Allison © 2000 Question An particle with a charge +2e and a mass of 4m p is on a collision course with a proton with a charge +e and mass m p. The only force acting is the electrostatic force. Which of the following statements is true about the magnitudes of the forces on the two particles? p Charge+2e+e Mass4m p mpmp A) F = F p B) 2F = F p C) 4F = F p D) F = 2F p E) F = 4F p

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Charles Allison © 2000 Question An particle with a charge +2e and a mass of 4m p is on a collision course with a proton with a charge +e and mass m p. The only force acting is the electrostatic force. Which of the following statements is true about the accelerations of the two particles? p Charge+2e+e Mass4m p mpmp A) a = a p B) 2a = a p C) 4a = a p D) a = 2a p E) a = 4a p

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Charles Allison © 2000 21-5 Coulomb’s Law Example 21-2: Three charges in a line. Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 3 (the -4.0 μC on the right) due to the other two charges.

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Charles Allison © 2000 21-5 Coulomb’s Law Example 21-3: Electric force using vector components. Calculate the net electrostatic force on charge Q 3 shown in the figure due to the charges Q 1 and Q 2.

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Charles Allison © 2000 Question What is the correct FBD for charge 3 where F 31 is the force on Q3 due to Q1 and F 32 is the force on Q3 due to Q2? a) b) c) d) +-+ Q1 Q2 Q3 3 F 31 F 32 3 33 F 31 F 32 F 31 F 32 F 31 F 32

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Charles Allison © 2000 21-6 The Electric Field Gravitational Field + -e Electric Field + + + –Units N/C –Direction of E is the direction a + test charge would go

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Charles Allison © 2000 The electric field is defined as the force on a small charge, divided by the magnitude of the charge: 21-6 The Electric Field

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Charles Allison © 2000 For a point charge: 21-6 The Electric Field ε 0 is the permittivity of the free space=8.85x10 -12 C 2 /N.m 2

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Charles Allison © 2000 Electric Field: point charge If we have a charge (or a system of charges) we can ask ourselves what the electric field is at any point in space, P, a distance r from the charge. -e P r Units: N/C +e P r

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Charles Allison © 2000 Force on a point charge in an electric field: 21-6 The Electric Field

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Charles Allison © 2000 Electric Field: system of charges If we have a system of charges we can ask ourselves what the electric field is at any point in space, P. In this case we find the Electric field due to each charge in the system at at that point, P, and we do a vector sum of these fields. q1 P r3r3 r1r1 q2 q3 r2r2

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Charles Allison © 2000 Electric Field: Two Charges We have two charges q1 = +7.0 µC and q2 = -8.0 µC a distance of 0.50 m to the right of q1. What is the electric field at a distance of 0.30 m to the right of q2? q1 P q2 r=0.5m r=0.30m k = 8.99x10 +9 Nm 2 /C 2 = coulomb’s constant

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Charles Allison © 2000 21-6 The Electric Field Example 21-7: E at a point between two charges. Two point charges are separated by a distance of 10.0 cm. One has a charge of -25 μC and the other +50 μC. (a) Determine the direction and magnitude of the electric field at a point P between the two charges that is 2.0 cm from the negative charge. (b) If an electron (mass = 9.11 x 10 -31 kg) is placed at rest at P and then released, what will be its initial acceleration (direction and magnitude)?

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