The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of 20 cm from its center is 1.5×10−5Tm. The magnetic moment of the dipole is _____ Am2. (Given : μ04π=10−7TmA−1)

For an axis perpendicular to the line connecting the+-5.00\\\\mu Ccharges at the midpoint of this line, find the torque (magnitude and direction) exerted on the dipole by the-10.00\\\\mu Ccharge,\\nFigure E21.55

21.55 - Three charges are at the corners of an isosceles triangle as shown in Fig. E21.55. The+-5.00\\\\mu Ccharges form a dipole. (a) Find the force (magnitude and direction) the-10.00\\\\mu Ccharge exerts on the dipole. (b) For an axis perpendicular to the line connecting the+-5.00\\\\mu Ccharges at the midpoint of this line, find the torque (magnitude and direction) exerted on the dipole by the-10.00\\\\mu Ccharge,\\nFigure E21.55

Derive the expresssion of the magnetic dipole

Consider a dipole with charge q = 1.65 nC and separation d = 0.549 m. What is the potential a distance x = 0.699 m from the center of this dipole at an angle θ = 63.7° with respect to the dipole axis, as shown in the figure?   V

Field and flux of a magnetic dipole. The magnetic field at a point M(r, θ) distant from a magnetic dipole m is expressed as B(M) = − µ0 4π ∇ m · r r 3  This formula is identical to that of the electric field produced by an electric dipole moment m, after changing µ0 into 1/0. q m i z r ur uq O O’ M a R’ We consider a small planar and circular loop of center O, radius a, carrying a current i and we use a spherical coordinate system (r, θ, ϕ) with the z-axis oriented along the magnetic dipole moment: m = muz. The expression of the gradient in spherical coordinates is as follow: ∇φ = ∂φ ∂r ur + 1 r ∂φ ∂θ uθ + 1 r sin θ ∂φ ∂ϕuϕ a. Express the corresponding magnetic dipole moment as a function of a and i.