wire shown at the right carries a current of A. The segment of the wire s L = 30

Question

wire shown at the right carries a current of A. The segment of the wire s L = 30cm long. Con- Y sider the magnetic field at the point P a distance d = 6cm from the end of the wire as drawn. Nat urally, all fields below must be reported as vectors. Carefully and clearly show all intermediate steps to your calculations. J (a)[3 pt(s) ]Compute the magnetic field p at P using the infinite straight wire approximation. x (b)[8 pt(s) ]Compute the magnetic field at point P approximating the segment with one segment using the finite current ele ment approximation. (c)[8 pt(s) ]Calculate the exact magnetic field at P starting from the Biot-Savart Law. (d)[2 pt(s) ]Do you expect either of the approximations in parts (a) and (b) to be very accurate? Why?

Explanation / Answer

current in the wire i=0.25 A

length of the wire l=30cm

distance between wire and point P is d=6cm

a)

for infinite straight wire approximation,

magnetic field at pont p is,

B=(uo*i)/(4pi*d)

B=(4pi*10^-7*0.25)/(4pi*0.06)

B=4.17*10^-7 T

b)

for finite straight wire approximation,

magnetic field at pont p is,

B=((uo*i)/(4pi*d))*sin(theta)

here,

sin(theta)=l/sqrt(l^2+d^2)

now,

B=((uo*i)/(4pi*d))*(l/sqrt(l^2+d^2))

B=((4pi*10^-7*0.25)/(4pi*0.06))*(0.3/(sqrt(0.3^2+0.06^2)

B=4.086*10^-7 T

c)

by using Biot-Savart law,

magnetic field due to finite length of wire at any pont P near the wire at distance d is,

B=((uo*i)/(4pi*d))*(sin(theta1)+sin(theta2))

here,

if point P is ad distance d at one end,

sin((theta2))=0 ( because, theta1=0)

and

sin(theta2)=l/sqrt(l^2+d^2)

now,

B=B=((uo*i)/(4pi*d))*(l/sqrt(l^2+d^2))

B=((4pi*10^-7*0.25)/(4pi*0.06))*(0.3/(sqrt(0.3^2+0.06^2)

B=4.086*10^-7 T

d)

very accurate value B is part(b),

because, the given wire has finite length

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