http://i44.tinypic.com/fp2dg.jpg A long uniformly charged thread (linear charge

Question

http://i44.tinypic.com/fp2dg.jpg A long uniformly charged thread (linear charge density = 1.5 ) lies along the axis in the figure.(Figure 1) A small charged sphere ( = -2.6 ) is at the point x=0cm, y=-5.0 cm A) What is the direction of the electric field at the point , ? and represent fields due to the long thread and the charge , respectively. Express your answer to two significant figures and include the appropriate units. B) What is the magnitude of the electric field at the point , ? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Call (7,7) cm point P. _____________________________________ The field at P from the line-charge is E1 = ?/(2p.e0.r) E1 = 1.5/(2p x 8.854x10^-12 x 0.07) = 3.85x10^11 N/C This has an x-component of zero and a y- component of 3.85x10^11 N/C ______________________________________ The distance PQ = v(12² + 7²) = 13.9cm The field at P from the charge at Q is E2 = Q/(4p.e0.r^2) E2 = -2.6/(4p x 8.854x10^-12 x 0.139^2) = -1.21x10^12 N/C (the minus sign just gives the direction as radially inwards to Q) From diagram and length PQ: sin(?) = 12/13.9 = 0.863 cos(?) = 7/13.9 = 0.504 Resolve E2 into components, note that E2 points from P to Q so the components will be negative. The x-component of E2 = -1.21x10^12cos(?) = -1.21x10^12 x 0.504 = -6.09x10^11N/C The y-component of E2 = -1.21x10^12sin(?) = -1.21x10^12 x 0.863 = -1.04x10^12 N/C _________________________________ Total of x-component = 0 + (-6.09x10^11) = -6.09x10^11 N/C Total of y-component = 3.85x10^11 + (-1.04x10^12) = -6.55x10^11 N/C Combine these total components with the help of a new small diagram. As the resultant is in the 4th quadrant, it is convenient to work out the angle relative to the -y axis initially. Let a be the angle of the resultant to the -y axis; mark this on the diagram, and you will see: tan(a) = (-6.09x10^11) / (-6.55x10^11) = 1.24 a = tan-1(0.93) = 46 degrees From the diagram you can see that measured clockwise from the x-axis, the final answer is 90 + 46 = 136. (For completeness/checking, the resultant = v[(6.09x10^11)² + (6.55x10^11)²] = 9.1x10^11N/C )

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