10. For the magnetic circuit of Fig. 10, the current i flows through the coil of N turns. The mean core length is _c, and the air gap length is _g. Assume no magnetic leakage. The flux crossing the cross-sectional area A. The relative permeability of core is μ_r. The permeability of air is μ_0. Find the flux in the air gap. (10%)

(4) NTPU Corp is committed to its quality program. It works with all areas of the company to establish sound quality programs within reasonable budget guidelines. For 2026, it has budgeted $1,000,000 for prevention costs and $900,000 for appraisal costs. Internal failure has a budget of $100 per failed item, while external failure has a total budget of $600,000. Product Testing has proposed to management a change in the 2026 budget for a new method of testing products. If management decides to implement the new method, $1.5 per unit of appraisal costs will be saved, up to a level of 150,000 tests. No additional savings are expected past the 150,000 level. The new method involves $95,000 in training costs and $65,000 in yearly testing supplies. Traditionally, 5% of all completed items have to be reworked. External failure costs average $120 per failed unit. The company's average external failures are 1% of units sold. The company carries no ending inventories. Required: How much do internal failure costs change, assuming 500,000 units are tested under the new method and it reduces the amount of unacceptable units in the manufacturing process by 40%?

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