Question

A point charge q1=+0.40 µC is located on the positive y axis at y = 8.0 cm, and a charge q2 = +0.65 µC is at the origin. A third charge q3 = -0.90µC is placed at x = 6.0 cm. Calculate: 21) the magnitude and direction of the electric field that exerts on the first charge by q2. 22) the magnitude and direction of the electric field that exerts on the first charge by q3. 23) the x-component of the net field that exerts on the first charge. 24) the y-component of the net field that exerts on the first charge.

Answer 1

Let the location of charges q1, q2, and q3 be at the points A, B, C respectively.

q1= 0.4 *10-6 C

q2 = 0.65*10-6 C

and

q3 = -0.9*10-6 C

Distance between q1 and q2 = r12 = 8 cm = 8*10-2 m

Distance between q1 and q3 = r13 = 10 cm = 0.1 m

Electric field on first charge (q1) exerted by q2= E12 = kq2/(r12)2 = 9*109*0.65*10-6/ (8*10-2)2 = 0.0914*107 N/C

the direction of the field is from q2 to q1. ( Along +ve y axis)

In vector form, E12 can be written as

21) Electric field on first charge (q1) exerted by q3= E13 = kq3/(r13)2 = 9*109*0.9*10-6/ (10-1)2 = 8.1*105 N/C

Since q3 is -ve, the direction of the field is from q1 to q3.

let this vector makes an angle with X-axis as shown in the figure.

This vector can be resolved into two components: along X-axis and along Y-axis

along positive X-axis

where

and

along -ve Y-axis

In vector form, the electric field can be written as

23. The x-component of the net electric field exerted on q1 =

E12x+E13x = 0+4.86*105 = 4.86*105 N/C

24.The Y-component of the net electric field exerted on q1=

E12y - E13y =9.14*105 - 6.48*105 = 2.66*105 N/C

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E12 = 9.14 * 1059

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cos A = 6/10 = 0.6

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E13 = E13 cos i + E13 sin 0(-;)

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