Question

A 0.30 T magnetic field pointing into the plane exists in the gray area. A wire with bends as shown is in the same plane, and a current of I = 5.0 A is directed to the right. Four segments of the wire, A- D, are identified. a) Sketch the force on each segment A, B, C, D with the length of the force vectors approximately indicating the magnitude of the force. [5 points] b) Calculate the direction and magnitude of the net magnetic force on the wire. [10 points] B = 0.30 Tin B C A D Yp0.50 m 2 0.50 m- my 0.50 m 0.50 m I

Answer 1

Magnetic force on a wire in the magnetic field is given by 7--7-7) Here, L is the length vector of the side of the loop. taken in the direction of the current and direction of the force is determined using right hand rule and will be in the direction of L x B Forces acting on each segment are shown below. "A F Since 1, L and B is same for all therefore magnitude of force on each segment will be same in the directions as shown above. Resolve the force FB and FC in the horizontal and vertical direction. Horizontal component will cancel out each other beacuse therefore magnitude is same but directions are opposite. Remaining components and FA and FD are in the same direction upward hence adds each other therefore net magnetic force on the wire will be in upward direction and it's magnitude is

B Fosinas Sin 45 FA 45 Folos Ficosa st Fnet = FA+Fpsin45 + F sin45 + FD FA = FB = Fc FD = Fo = ILB = (5) * (0.5) * (0.3) = 0.75N F net = Fo + Fosin45 + Fosin45 + Fo F. net (2 + V2)*(0.75) Fnet = 2.561N Direction upward