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Figure 16.15 is an end view of a triangular prism, whose three faces are labeled by the vectors dA1, etc. (The magnitude of dA1 is the area of the corresponding surface and the direction is normal to it. There are two more faces parallel to the plane of the paper, but these do not concern us.) The ends of the three faces form a closed triangle. Explain clearly why this implies that dA1+ dA2+dA3= 0.
Figure 16.15
Prove the same result using the formula inside the back cover for ∇2 in spherical polar coordinates. (Obviously, this second proof is much simpler, but the hard work is hidden in the derivation of the formula for ∇2.)
Design the sequence counter using D flip-flops. Include inyour design the state diagram, state transition table, legend, nextstate equations, and schematic diagram. The counting sequence is
A helical spring is fabricated by wrapping wire ¾ in. in diameter around a forming cylinder 8 in. in diameter. Compute the number of turns required to permit an elongation of 4 in. without exceeding a shearing stress of 18 ksi. G = 12 × 106 psi.
Take the concepts learned in a classroom
(a) Howmany 256M X 16 RAMchips are needed to provide amemory capacity of 8 GB (b) How many address lines are needed to address this memory (c) How many address lines need to go to each chip
an 8 pole synchronous motor produces a full load torque of 25 foot pounds, fed from a 60hz source and is now operating at 60% eff. What is the energy cost if the motor ran for a 8000 hrs/yr and the electrical energy cost were $.09/kWh.
If we define the resolution of a Digital-to-Analog Conversion (DAC) device to be the reciprocal of its number of logic states in percentage, what will be the resolution of an 8-bits DAC device
Find an expression for the scalar electric potential at any point on the axis of the ring. Indicate clearly your coordinate system and its geometry. Check the limiting case as the field point recedes to infinity.
In terms of good desgn practice , what is the number of receptacles allowed on a general purpose 15 A 120V circuit. A 20A and 120V circuit. What are the requirements for the circuit supplying bathroom in residences
A sensitive IC (integrated circuit) on a circuit board is located 1m from a long power line carrying 10A. The power line generates a magnetic field. You can place a trace on a circuit board with current running parallel to the power line to cancel..
Two charged concentric spherical shells have radii 10.0cm and 15.0cm. The charge on the inner shell is 4.00X10^-8C, and that on the outer shell is 2.00X10^-8C. Find the electric field (a) at r = 12.0cm and (b) at r = 20.0cm.
What crystal growth method is used for today's high brightness LEDs and what are the leading manufacturers of the tools for this growth method.
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