Suppose there are two electric charges in 2D planeR2; one is on y-axis and the other is on x-axis:

45km 0 p1:=0,p2:=30km.(1)

Thechargesareq1=4.5Catp1andq2=3.0Catp2.

(a) Determine the electric field generated byq1at the origin.

(b) Determine the electric field generated byq2at the origin.

(c) Assuming the superposition principle, determine the electric field at the origin, namely the magnitude of the field and direction.

Note that Coulomb constantkis about 9.0109N m2C2. For each question, you must specify the relevant unit in SI.

2. Momentum and Newton's Second Law of Motion

Let us recall Newton's second law of motion, namely the equation of motion from momentum perspective, see8.1 and8.2. Letm >0 be a mass andp1be the initial linear momentum. Within a finite time interval t >0, the motion state changes under some force. LetFbe the average force acting onmin the time interval t.

(a) The productFt- impulse - is a good characteristic of the effect of the actual force in the time interval t, see Figure 8.2. Determine the unit of the impulse.

(b) If we consider the change of linear momentum, the corresponding "flow" quantity is the impulseI:=Ft:

pIGGp(2)12

Choose either + orand explain why. (c) With these stock-flow relation, discuss the condition(s) for linear momen-

tum conservation.

3. Kirchhoff's Rules Repeat the same analysis of Example 21.5, see Figure 21.25, with

1

E1=18 V, E2= 45 VE1= 18 V, E2=45 V

Note that the negative voltage means we physically swap the polarity of the battery cell in the circuit.