9. Determine the location i of the centroid C of the shaded area that is part of a circle having a radius r. a
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- 2. Given the vectors à = i - j+ k and b = 2i - j- 2k, determine the following: a. the scalar projection and vector projection of å on b b. the angle that b makes with each of the coordinate axes c. the area of the parallelogram formed by the vectors a and b1. What is the electric flux through a sphere that has a radius of 1 m and carries a charge of +5μC at its center? 2. A solid ball with 0.5 meters radius has +10 μC electric charge in its center. Determine the electric flux pass through the solid ball.Q1. a- a conducting sphere with radius 5 cm charged with 2 nC, find the electric field at 10 cm far from the center. b- an object charged with 4 C placed on electric field then it effect 28 N , find the magnitude of the electric field.
- H and I pleaseQ2. Locate the centroid of the plane area shown. 14 in.- 25 in. 5 in 16 in. 5.5 in 10 in 7.5 in3. Assume a solid conductor is placed next to a negatively charged sphere. This causes the surface of the conductor near the sphere to become positively charged so that the net electric field inside the conductor is zero. Now we cut a hole so that it is entirely encased by the conductor. а. Does removing part of the inside of the conductor affect the electric field? cross-section of 3D conductor b. What the electric field inside the hole? c. Explain why sensitive equipment are often placed inside conductors. For example, circuit boards are typically shipped in foil-lined bags while cell phone signals are weaker inside warehouses with metal sides.
- A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 5 ft from the house, the base is moving away at the rate of 36 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? y 13-ft ladder y(t) x(t) X5. Let F = -9zi+ (xe"² – 2xe²²)+ 12 k. Find ſg F .dø and let S be the portion of the plane 2x + 3z = 6 that lies in the first octant such that 0 < y < 4 (see figure to the right), oriented upward. (a) Explain why the formula F à cannot be used to find the flux of F through the surface S. Please be specific and use a complete sentence.3. GAUSS'S LAW A uniform electric field with a magnitude of 1.25x10° N/C passes through a rectangle with sides of 2.50 m and 5.0 m . If the electric flux through the rectangle is 6.6x105 Nm2/C , find the angle between the electric field vector and the vector normal to the rectangular surface ?