Question

A long, straight wire lies along the z−axis and carries a 4.10 −A current in the +z−direction. Find the magnetic field (magnitude and direction) produced at the following points by a 0.400 −mm segment of the wire centered at the origin.

Part A

x=2.00m,y=0, z=0

Enter your answers numerically separated by commas.

Bx,By,Bz =

___

T

Part B

x=0, y=2.00m, z=0

Enter your answers numerically separated by commas.

Bx,By,Bz =

___

T

Part C

x=2.00m, y=2.00m, z=0

Enter your answers numerically separated by commas.

Bx,By,Bz =

___

T

Part D

x=0, y=0, z=2.00m

Enter your answers numerically separated by commas.

Bx,By,Bz =

___

T

Answer 1

(a)

Magnetic field due to a segment of wire,

B = u0*l dl x / 4r^3

when = 2 i,

B =  410^-7*4.1*0.4*10^-3k x 2i /  4*2³

B = 0.41*10^-10 T (j)

(Bx , By , Bz) = (0 , 0.41*10^-10 , 0) T

(b)

= 2 j

B =  410^-7*4.1*0.4*10^-3k x 2j /  4*2³

B =0.41*10^-10 T (-i)

(Bx , By , Bz) = (-0.41*10^-10 , 0 , 0) T

(c)

= 2 i , 2 j

r = sqrt (2^2 + 2^2) = 2.83 m

B =  410^-7*4.1*0.4*10^-3k x (2i + 2j) /  4*(2.83)³

B = (0.144*10^-10 j -  0.144*10^-10 i ) T

Magnitude of magnetic field, B = sqrt (Bx^2 + By^2)

B = 0.204*10^-10 T

(Bx , By , Bz) = (- 0.144*10^-10 , 0.144*10^-10 , 0) T

(d)

= 2 k

B =  410^-7*4.1*0.4*10^-3k x 2k /  4*2³

B = 0

(Bx , By , Bz) = (0 , 0 , 0) T