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SP212 Worksheet 4 Ch 22.(6,7) Charges and Dipoles in an electric field Problem 1 A disk of radius R has a uniform surface charge of σ = 5µC/m2 smeared across it. A proton is released from a point on the disk’s axis above the disc. What is the acceleration of the proton if it is released from the following distances: a) released from a distance z = R b) released from a distance z = R/2 c) released from a distance z = 20R proton has a mass of 1.67 × 10−27 kg and the same charge as an electron, 1.61 × 10−19 C. HINT: The electric field due to a uniformly charged disk is E = 2σ0 1 − √z2z+R2 where k = 1 4π0 2 and 0 = 8.85 × 10−12 NCm2 This problem is relevant for HW L4 problem 48. Problem 2 A charge of size −4µC is placed at the origin of an xy coordinate system. Another charge of size +4µC is placed at the position x = 2 × 10−10 m and y = −4 × 10− 10 m. a) In component form (i.e. using î and ĵ) what is the dipole moment of this two charge system? What is the magnitude of the dipole moment? ~ = 5000î N/C. What is the potential energy of b) This dipole is placed in a constant electric field E the dipole? What is the torque (as a vector) acting on the dipole? c) If I reached down ad rotated this dipole by 180◦ , how much work would I have to do on the dipole? TIP: remember that the work done by a conservative force is given by W = −∆U This problem is relevant for HW L4 problems 59 and 83.