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Phys102 Term: 131 Online HW-Ch23-Lec03 Q1: Which of the following graphs represents the magnitude of the electric field as a function of the distance from the center of a solid charged conducing sphere of radius R? Ans: E Q2: A proton is shot directly toward the center of a large metal plate that has surface density 2.0 x 10-6 C/m2. If the initial kinetic energy of the proton 1.6 x 10-17 J and if the proton is to stop just as it reaches the plate, how far from the plate must be launched? (Give the answer in three significant figures and SI units) Ans: We take the initial direction of motion of the proton to be positive. Then, the electric field is given by E = σ/ε 0 , where σ is the surface charge density on the plate. The force on the electron is F = –eE = –eσ/ε 0 and the acceleration is: a= F eσ = − m ε 0m where m is the mass of the proton. The force is constant, so we use constant acceleration kinematics. If v 0 is the initial velocity of the proton, v is the final velocity, and x is the distance traveled between the initial and final positions, then v 2 − v02 = 2ax. Set v = 0 and replace a with –eσ/ε 0 m, then solve for x. We find: v 2 ε 0 mv02 − 0 = x= . 2a 2eσ Now 1 2 mv02 is the initial kinetic energy K 0 , so = x ε 0 K0 = eσ (8.85 ×10 C / N ⋅ m )(1.60 ×10 J ) (1.60 ×10 C )( 2.0 ×10 C/m ) −12 2 −19 −17 2 −6 2 = 4.43 × 10−4 𝑚 KFUPM-Physics Department 1 Phys102 Term: 131 Online HW-Ch23-Lec03 Q3: A charge is distributed uniformly along a long straight wire. If the electric field 4.0 cm from the wire is 40 N/C, then the electric field 8.0 cm from the wire is (Give the answer in two significant figures and SI units) Ans: E1 = λ 2π × ε 0 × r1 E2 = λ 2π × ε 0 × r2 E2 r1 4 = = = 0.5 E1 r2 8 ⇒ E2 = 20 N/C KFUPM-Physics Department 2