Question

3) Suppose there is a current of lo in +x direction in an infinity long wire. A finite wire along yaxis with the length of L and the mass m, is located between y= -L/2 and y=L/2 and it has current of 1 in +y direction. a) Find force and/or torque due to current lo on the finite wire along the y-axis. b) Find acceleration and/or angular acceleration due to current lo on the finite wire along the y-axis.

Answer 1

AtY +42 AI, -42 AL F -Y a) Let the force acting on ends of wire having finite length is, For length y=+421 F- ILBsino general forma B - Lolo 16 = 90 Where, I = I, , L= 1 / 1 Ar(E) ***F= 11(E) la 19) singo F= Mo Io Is 2. Ir similarly, for length y = - 4 - 2 F=- elo to I 2IT Both the forces produces torque :.0=rfsina = (1 - (- + 2)) = L, O=go --TEL(40.5 41) T= Mo Io I L) 2T b) Due to nonzero torque wire rotates with angular acceleration we have c = I2 => x = 0 Wire is considered) 'ML2 (ME as a thin rod -.x= 12 a = Molo II L x 2T ML2 id=6lolol radesh TTML This is the angular acceleration due to current To acting on wire having finite length,