Physics

Problem

A magnetic dipole of moment

\mu = 0.10\,\text{A\,m}^2

lies in the

x\!y

–plane. The region contains two uniform magnetic fields:

\mathbf{B}_1

of magnitude

0.05\,\text{T}

directed along the positive

x

–axis and

\mathbf{B}_2

of magnitude

0.12\,\text{T}

directed along the positive

y

–axis. a. (i) Treating the dipole moment vector as confined to the

x\!y

–plane and making an angle

\phi

with the

x

–axis, obtain an expression for the potential energy of the dipole as a function of

\phi

. b. (ii) Determine the value of

\phi

for which the potential energy is minimum. Show all necessary steps. c. (iii) Calculate this minimum potential energy.