Point charge q_1 = -5.10 nC is at the origin and point charge q_2 = +3.40 nC is
ID: 1413776 • Letter: P
Question
Point charge q_1 = -5.10 nC is at the origin and point charge q_2 = +3.40 nC is on the x-axis at x = 2.85 cm. Point P is on the y-axis at y = 3.90 cm. Calculate the electric fields E^rightarrow_1 and E^rightarrow_2 at point P due to the charges q_1 and q_2. Express your results in terms of unit vectors. E^rightarrow_1 =_______N/C Icirc +______N/C jcirc E^rightarrow_2 =_______N/C Icirc +_______N/C jcirc Use the results of part (a) to obtain the resultant filed at p, expressed in unit vector form. E^rightarrow =______N/C iciec +______N/C jciecExplanation / Answer
1) Point charge q1= -5.10*10^-9 C is at the origin
Point charge q2 = +3.40*10^-9 C is at x= 2.85*10^-2 m.
Point P is on the y-axis at y=3.9*10^-2 m.
Electric field due to q1at P=E1 =9*10^9*5.1*10^-9 /(3.9*10^-2)^2
E1=3.0177*10^4 N/C
As charge q1 is negative E1 is in negative y direction
In vector notation , E1 =[ 3.0177*10^4 N/C ](-j)
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Point charge q2= +3.40nC is on the x-axis at x = 2.85cm.
Distance of q2 from point P = r!=5 cm = 5*10^-2 m
Vector r! = -0.03i^ +0.039j^
Electric field due to q2at P=E2 =9*10^9*3*10^-9 /(5*10^-2)^2
E2 = 1.08*10^4 N/C in a direction from q2 to P making angle O with negative x axis
tan O=4/3
Angle =O= 53 degree,
cos53=0.6, and sin53=0.8
Component of E2 in negative x axis direction =1.08*10^4 cosO
Component of E2 =1.08*10^4 *[0.6] =6.48*10^3 N/C
Component of E2 in negative x axis direction=6.48*10^3N/C(-i)
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Component of E2 in +y axis direction =1.08*10^4 sinO
Component of E2 in +y axis direction =1.08*10^4*[0.8]
Component of E2 in +y axis direction =8.64*10^3N/C( j)
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In vector form ,E2 =6.48*10^3N/C(-i)+8.64*10^3N/C( j)
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b) The resultant field at P, expressed in unit vector form,
E = E1+E2
E= 2.8125*10^4 N/C(-j)+6.48*10^3N/C(-i)+8.64*10^3N/C( j)
E= 28.125*10^3 N/C(-j)+6.48*10^3N/C(-i)+8.64*10^3N/C( j)
The resultant field at P= - 6.48*10^3N/C(i)-19.485*10^3N/C(j)
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Resultant field of magnitude 20.5342*10^3 N/C makes an angle of 71.6 degree anticlockwise with negative x - axis
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