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Please take note that it is 2i.

Please take note that the qn is 2i

maps the We know from pages 108-109 in the Notes that the transformation z =w-w? straight line segment -2 5 Im(2) 5 2 in the z-plane into the circle [w] =1 in the w-plane. In this question you will be considering a closely related transformation: w = 2i(z-z ') which maps the unit circle (21 = 1 in the z-plane into a line segment in the w-plane. In particular, you will use this transformation to construct the electric field outside the line segment in the w-plane (which is assumed to be a charged plate). We know that the electric field outside the circle (21=1 (if this was a ring of electric charge) is a set of radial lines. We can represent these radial lines by the parametric equation z(t) = t exp(io) where t is a parameter that ranges from 1 to co, and 0, is a constant (which has a different value on each radial line). So what you are asked to do in this question is: Plot the 12 curves w(t)= 2i(z - z-') in the w-plane, where z(t)=texp(io) for the 12 values 0. =1/8,91/4,+37/8, 51/8,+31/4 and 77/8, and the parameter t ranges from 1 to 5 on each curve. (You should plot at least 5 points on each curve, for example the points with t = 1,2,3,4 and 5, then join these points together.) maps the We know from pages 108-109 in the Notes that the transformation z =w-w? straight line segment -2 5 Im(2) 5 2 in the z-plane into the circle [w] =1 in the w-plane. In this question you will be considering a closely related transformation: w = 2i(z-z ') which maps the unit circle (21 = 1 in the z-plane into a line segment in the w-plane. In particular, you will use this transformation to construct the electric field outside the line segment in the w-plane (which is assumed to be a charged plate). We know that the electric field outside the circle (21=1 (if this was a ring of electric charge) is a set of radial lines. We can represent these radial lines by the parametric equation z(t) = t exp(io) where t is a parameter that ranges from 1 to co, and 0, is a constant (which has a different value on each radial line). So what you are asked to do in this question is: Plot the 12 curves w(t)= 2i(z - z-') in the w-plane, where z(t)=texp(io) for the 12 values 0. =1/8,91/4,+37/8, 51/8,+31/4 and 77/8, and the parameter t ranges from 1 to 5 on each curve. (You should plot at least 5 points on each curve, for example the points with t = 1,2,3,4 and 5, then join these points together.)

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