Question

Electric potential difference EM 105 B. Shown at right are four points near a positively charged rod. Points W and Yare equidistant from the rod, as are points X and Z. A charged particle with mass m3x 10 kg is released from rest at point W and later is observed to pass point X 1. Is the particle positively or negatively charged? Explain. 2. Suppose that the magnitude of the charge on the particle is 2 x 10 C and that the speed of the particle is 40 m/'s as it passes point X. a. Find the change in kinetic energy of the particle as it travels from point W to point X. Find the work done by the electric field on the particle between point W and point X (Hint: See part D of section I.) b Find the electric potential difference between point Wand point X. A c. d. If the same particle were released from point Y, would its speed as it passes point Z be greater than, less than, or equal to 40 m/s? Explain. Suppose that a second particle with the same mass as the first but nine times the charge (ie., 18 × 10 3. C) were released from rest at point W a. Would the electric potential difference between points W and X change? If so,how, if not, why not? Would the speed of the second particle as it passes point X be greater than, less than or equal to the speed of the first particle as it passed point X? Explain b.

Answer 1

Since the rod is positively charged it produces field towards W as shown. Hence a +ve charge particle at W will only experience a force towards X otherwise if it was -ve then it would have moved towards the rod. Hence the particle is +vely charged Delta KE = 1/2 times 3 times 10^-8(40)^2 = 2400 times 10^-8 J Work done by E field = Change in KE = 2400 times 10^-8 J Work done = q Delta V = Delta KE q(V_w - V_x) = 2400 time 10^-8 V_w - V_x = 2400 times 10^-8/2 times 10^-6 = 12 V Since the distance Y_0 = W_0 Z_0 = X_) and field is along OZ and OX it is similar, hence speed at z when released from y will be equalto 40 m/s \r\n electric potential at a point is a function of the source creating the potential and is not affected by the quantity of charge placed at that point,