A microcircuit must be supplied with DC voltage and current in order to operated as designed....

   
 
 

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A microcircuit must be supplied with DC voltage and current in order to operated as designed. In the circuit shown in figure 2, the wires carrying a DC supply current IDc form a square loop. The length of each side is L = (20 + x) um and the DC current is Ipc = 0.1 (1 + 8) mA. DC supply wires L/2 3L/4 L/4 L/2 Figure 2. Wires carrying a DC supply current Ipc in a microcircuit form a square loop. (i) Find the magnitude of the net magnetic field (H and B) at the point P as shown in this figure. Take u = 1. (ii) Estimate the net Ampere's force on wire 1 acting from wire 2 (the same as on wire 2 acting from wire 1), neglecting the effects of all other wires and neglecting the finite length of the wires. (You can make any approximations, but you should clearly explain them.) Is this force attracting or repulsive? Is the force strong or weak? Hint 3: In order to answer the latter question, you can compare net Ampere's force acting on the wire with other examples from Electromagnetics, for instance, with electrostatic Coulomb's force. If a current I flows in a wire, at a given instance of time this wire carries a charge q = I·L/ ve where L is the length of the wire and ve is the drift velocity of charge carriers in the wire. Typical ve in metals is 2 x 104 to 5 x103 m/s. Simplifying and replacing each wire by a point charge, it is possible to estimate Coulomb's force between the wires. Hint 4: If you are not sure how to derive the magnetic field due to a finite conductor (problem 2 of this set), you can use the following formulae (this will allow you to obtain some marks): I (sin B, + sin B,), B= 4πd Moll,I -(sin B, + sin B,) 4лd Z2 H = I ZA or y I (cos0, +cos0,), B= 4rd (cos0, +cos0,) 4πd H = a, = 0, -Z1 A microcircuit must be supplied with DC voltage and current in order to operated as designed. In the circuit shown in figure 2, the wires carrying a DC supply current IDc form a square loop. The length of each side is L = (20 + x) um and the DC current is Ipc = 0.1 (1 + 8) mA. DC supply wires L/2 3L/4 L/4 L/2 Figure 2. Wires carrying a DC supply current Ipc in a microcircuit form a square loop. (i) Find the magnitude of the net magnetic field (H and B) at the point P as shown in this figure. Take u = 1. (ii) Estimate the net Ampere's force on wire 1 acting from wire 2 (the same as on wire 2 acting from wire 1), neglecting the effects of all other wires and neglecting the finite length of the wires. (You can make any approximations, but you should clearly explain them.) Is this force attracting or repulsive? Is the force strong or weak? Hint 3: In order to answer the latter question, you can compare net Ampere's force acting on the wire with other examples from Electromagnetics, for instance, with electrostatic Coulomb's force. If a current I flows in a wire, at a given instance of time this wire carries a charge q = I·L/ ve where L is the length of the wire and ve is the drift velocity of charge carriers in the wire. Typical ve in metals is 2 x 104 to 5 x103 m/s. Simplifying and replacing each wire by a point charge, it is possible to estimate Coulomb's force between the wires. Hint 4: If you are not sure how to derive the magnetic field due to a finite conductor (problem 2 of this set), you can use the following formulae (this will allow you to obtain some marks): I (sin B, + sin B,), B= 4πd Moll,I -(sin B, + sin B,) 4лd Z2 H = I ZA or y I (cos0, +cos0,), B= 4rd (cos0, +cos0,) 4πd H = a, = 0, -Z1

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