Question

Instructor HW7 Ch. 26 Electric Potential & EPE You must show all work to receive max credit y(m 3. A charge q+2* 10 C is located at (-2m,-2m) and 4-5 10 C is located at (+3m, +1m) Consider these charges fixed in place. a. Find the electric potential at point P, (1m,2m) Make sure that you draw a diagram showing the electric field and its components. P b. Suppose that a charge q,- +4*10 C is initially far away and is later at point P at one instant in time. What is the change in the potential energy of the system of three charges (from qu being far away to when q, is at point P)? What was the work done by the electric field of q and q; on qs during this time? If there are no external forces, what is the change in the kinetic energy of q? If the initial speed of q, is 300m/s and its mass is 2 1012 kg what is its speed as it goes through +x (m) point P?

Answer 1

Part A

Electric potential is defined as

ke

for 1 and g2

ke 9 x 109 Nm2 C2

r 2m 1m) (-2m 2m 5 m (distance from q to P)

T (1m 3m) (2m 1m) = 2.24 m (distance from q to P)

substituting

-5 x 10 2 x 10 V12 (9 x 10) =-1.65 x 106 V 2.24

Part B

$\Delta U=U_f-U_i$

$U_i=0$

Uf=3V12

$U_f=\left ( 4\times 10^{-4}\:C \right )\left ( -1.65\times 10^{6}\:V \right )=-660\:J$

The work done is

$W=F_ed$

$for\:q_1:$

$W_{13}=\left ( k_e\frac{\left | q_1 \right |\left | q_3 \right |}{r_{1}^{2}} \right )r_1=\left ( 9\times 10^{9} \right )\left ( \frac{\left ( 2\times 10^{-4} \right )\left ( 4\times 10^{4} \right )}{5} \right )=144\:J$

$W_{23}=\left ( k_e\frac{\left | q_2 \right |\left | q_3 \right |}{r_{2}^{2}} \right )r_2=\left ( 9\times 10^{9} \right )\left ( \frac{\left ( 5\times 10^{-4} \right )\left ( 4\times 10^{-4} \right )}{2.24} \right )=803.57\:J$