Phy problem...electricity3

(a)(i) Dipole moment of current loop
= 0.2 x [pi x 0.08^2] A.m^2 = 4.021 x 10^ -3 A .m^2
Hence, magnetic dipole moment M = (4.021x10^-3).(0.6i - 0.8j)

Torque on the loop
= M x B
= [(2.413 x 10^-3)i - (3.217x10^-3)j] x (0.25i + 0.3k) N.m
= -(9.651x10^-4)i -(7.239x10^-4)j+ (8043x10^-4)k N.m

(ii) Energy of the loop
= -M.B
= - [(2.413 x 10^-3)i - (3.217x10^-3)j].(0.25i + 0.3k) J
= -6.03x10^-4 J

(b) The equation for calculating magnetic field B at one end of a finite current carrying wire is,

B = [(uo)i/(4.pi.R)].[x/sqrt(x^2+R^2)]
where uo is the permeability of free space
i is the current
R is the perpendicular distance from the wire of length x
"sqrt" stands for "square-root"

Now, taking upward direction of magnetic field as +ve
Field at point P
B = [(uo)(13)/4.pi.a].[-a/sqrt(a^2+a^2) -a/sqrt(a^2+a^2)] + [(uo).(13)/4.pi.2a].[2a/sqrt(4a^2+4a^2) + 2a/sqrt(4a^2+4a^2)] T

B = [(uo).(13)/4.pi.a].[-sqrt(2)] + [(uo).(13)/4.pi.a].[1/sqrt(2)] T
B = [(uo).(13)/4.pi.a].(-0.7071) T
B = -1.96x10^-5 T