Three point charges (Q1= -3.5 uC, Q2= 2.5 uC and Q3= 4.5uC) arearranged as shown

Question

Three point charges (Q1= -3.5 uC, Q2= 2.5 uC and Q3= 4.5uC) arearranged as shown in Figure P4. Find the net electricpotential at point P. Calculate the work done to bring a protonfrom infinity to Point P. If released from Point P, calculatethe velocity of the proton.

Three point charges (Q1= -3.5 uC, Q2= 2.5 uC and Q3= 4.5uC) arearranged as shown in Figure P4. Find the net electricpotential at point P. Calculate the work done to bring a protonfrom infinity to Point P. If released from Point P, calculatethe velocity of the proton.

Explanation / Answer

the net electric potential at point P is V = V1 + V2 + V3---------(1) V1 = k * (Q1/r1) k = (1/4o) = 9 * 109Nm2/C2 Q1 = -3.5 C = -3.5 * 10-6 C r1 = L + L = 2L = 2 * 1.5 = 3 m V2 = k * (Q2/r2) Q2 = 2.5 C = 2.5 * 10-6 C r2 = (L2 + L2)1/2= 2L = 2 * 1.5 = 1.414 * 1.5 m = 2.1m and V3 = k * (Q3/r3) Q3 = 4.5 C = 4.5 * 10-6 C r3 = ((2L)2 +L2)1/2 = 5L = 2.236 * 1.5 m = 3.3m the work done to bring a proton from infinity to Point Pis W = V * q the value of V is obtained from equation (1) and q = 1.6 *10-19 C when released from point P,the velocity of the proton is W = (1/2)m * v2 or v = (2W/m)1/2 m = 1.67 * 10-27 kg Q1 = -3.5 C = -3.5 * 10-6 C r1 = L + L = 2L = 2 * 1.5 = 3 m V2 = k * (Q2/r2) Q2 = 2.5 C = 2.5 * 10-6 C r2 = (L2 + L2)1/2= 2L = 2 * 1.5 = 1.414 * 1.5 m = 2.1m and V3 = k * (Q3/r3) Q3 = 4.5 C = 4.5 * 10-6 C r3 = ((2L)2 +L2)1/2 = 5L = 2.236 * 1.5 m = 3.3m the work done to bring a proton from infinity to Point Pis W = V * q the value of V is obtained from equation (1) and q = 1.6 *10-19 C when released from point P,the velocity of the proton is W = (1/2)m * v2 or v = (2W/m)1/2 m = 1.67 * 10-27 kg Q2 = 2.5 C = 2.5 * 10-6 C r2 = (L2 + L2)1/2= 2L = 2 * 1.5 = 1.414 * 1.5 m = 2.1m and V3 = k * (Q3/r3) Q3 = 4.5 C = 4.5 * 10-6 C r3 = ((2L)2 +L2)1/2 = 5L = 2.236 * 1.5 m = 3.3m the work done to bring a proton from infinity to Point Pis W = V * q the value of V is obtained from equation (1) and q = 1.6 *10-19 C when released from point P,the velocity of the proton is W = (1/2)m * v2 or v = (2W/m)1/2 m = 1.67 * 10-27 kg Q3 = 4.5 C = 4.5 * 10-6 C r3 = ((2L)2 +L2)1/2 = 5L = 2.236 * 1.5 m = 3.3m the work done to bring a proton from infinity to Point Pis W = V * q the value of V is obtained from equation (1) and q = 1.6 *10-19 C when released from point P,the velocity of the proton is W = (1/2)m * v2 or v = (2W/m)1/2 m = 1.67 * 10-27 kg m = 1.67 * 10-27 kg

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