8.02X Electricity and Magnetism

Byh=0.1mxw=0.3mFor each wire,µ0Iµ0IB = =2πr 2 22 π h + w /2( )And the y component:w µ0IwBy= B =2 2h + w π h + w2 2( )By symmetry, all wires contribute the same By, therefore in totalBB4µIw0yTotal= 4 = ⇒y2 2π ( h + w )( 2 + 2 ) 8π( 0.1 2 + 0.32)Bπh wI = = = ×µ w π−7404× 4 × 10 × 0.361.7 10 A(c) Again using pictures and words show that you get repulsion if the currents inthe two wires run anti-parallel.The magnetic field created by wire 1 at wire 2is shown in figure.The force on wire 2 is given by F = IL×BWhich is in the +x direction: repulsionyxI1I2(d) . Assume that the field is homogenous at 8T over a cross-section of 200 cm2 .What is the total energy stored in the magnetic field of all dipoles combined?The energy density of magnetic field is2Bu =2µ0For each magnet, the energy stored isU = uV2