Magnetic field due to parallel wires 1. The problem statement, all variables and given/known data Two very long thin wires carrying equal and opposite currents +/-I are p laced parallel to the x-axis at y=0 and z=+/-a. Find an expression for B field at a point P in the xy-plane (z=0) and show that its maximum gradient occurs for y = a/sqrt(3). 2. Relevant equations Field due to long wire at distance d away: B=(mu_0*I)/(2*PI*d) 3. The attempt at a solution By symmetry, i expect B field components to cancel except in y direction..So i end up getting total field: B=B_y=(mu_0*I)/(PI*d) * cos(theta) where theta is the angle that d makes to the y axis. Because of geometry of situation, this is equivalent to saying: B=B_y=(mu_0*I*y)/(PI*d^2) Then for the gradient to be maximized, I need maximum of: dB/dtheta=-(mu_0*I)/(PI*d) * sin(theta) ...which should occur when sin(theta) is a max...but i dont understand how i could show that the maximum is for y = a/sqrt(3) any thoughts..? thankyou!!