A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its centre: (a) increases as r increases for r < R (b) decreases as r increases for 0
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- A charge of 30C is distributed uniformly a spherical volume of radius 10.0 cm. Determine the electric field due to this charge at a distance of (a) 2.0 cm, (b) 5.0 cm, and (c) 20.0 cm from the center of the sphere.Determine if approximate cylindrical symmetry holds for the following situations. State why or why not. (a) A 300-cm long copper rod of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (b) A 10-cm long copper of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (c) A 150-cm wooden rod is glued to a 150-cm plastic rod to make a 300 cm long rod, which is then painted with a charged paint so that one obtains a uniform charge density. The radius of each rod is 1 cm, and we seek an electric field at a point that is 4 cm from the center of the rod. (d) Same rod as (c), but we seek electric field at a point that is 500 cm from the center of the rod.The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball's center and has magnitude 4.0102 N/C. How much charge is on the surface of the ball?
- An arc subtends an angle a at the center. If radius of circle is R and the arc has uniform charge then value ER of at the center is (where E = Electric field, V = Potential) V sin (b) sin 2 sin (d) sin a (a) a (c) 2aThe general form of Gauss's law describes how a charge cre- ates an electric field in a material, as well as in vacuum: Tin E · dA = where e = Ke, is the permittivity of the material. (a) A sheet with charge Q uniformly distributed over its area A is sur- rounded by a dielectric. Show that the sheet creates a uni- form electric field at nearby points with magnitude E = Q/2 Ae. (b) Two large sheets of area A, carrying opposite charges of equal magnitude Q, are a small distance d apart. Show that they create uniform electric field in the space between them with magnitude E = Q/Ae. (c) Assume the negative plate is at zero potential. Show that the positive plate is at potential Qd/Ae. (d) Show that the capacitance of the pair of plates is given by C = Ae/d = KA€,/d.(c) d) 2R R. R. R. Two uniform line charges of = 4n C/m each are parallel to the z-axis at (0, 4)m and (0, -4)m. Magnitude of electric field at points (+4, 0, 0) is (a) 9 V/m (b) 18 V/m C4.5 V/m (d) 9/2 V/m
- A proton and electron separated by 2× 10^-10 m form an electric dipole, look figure. Useexact formula to calculate the electric field on t he X-axis at a distance 20 × 10^-10 m to the rightof the dipole’s center?A point charge q=5C is situated at a long distance r=15m on axis from one end of a thin no conducting rod of length L=2m (r≫L) having a charge Q=6C (Uniformly distributed along its length). The magnitude of electric fied at the point charge q will feel is:(a) A small Styrofoam bead with a charge of -60.0 nc is at the center of an insulating plastic spherical shell with an inner radius of 20.0 cm and an outer radius of 34.0 cm. The plastic material of the spherical shell is charged, with a uniform volume charge density of -1.50 pC/m³. A proton moves in a circular orbit just outside the spherical shell. What is the speed of the proton (in m/s)? m/s (b) What If? Suppose the spherical shell carries a positive charge density instead. What is the maximum value the charge density (in µC/m³) the spherical shell can have below which a proton can orbit the spherical shell? µC/m3
- (a) By what distance are the plates separated? b) What is the magnitude of the surface charge density on one of the plates?(a) A small polystyrene bead with a charge of -60.0 nC is at the center of an insulating glass spherical shell with an inner radius of 20.0 cm and an outer radius of 34.0 cm. The glass material of the spherical shell is charged, with a uniform volume charge density of -1.70 µC/m3. A proton moves in a circular orbit just outside the spherical shell. What is the speed of the proton (in m/s)? m/s (b) What If? Suppose the spherical shell carries a positive charge density instead. What is the maximum value the charge density (in µC/m3) the spherical shell can have below which a proton can orbit the spherical shell? HC/m3Common static electricity involves charges ranging from nanocoulombs to microcoulombs. (a) How many electrons are needed to form a charge of –2.00 nC (b) How many electrons must be removed from a neutral object to leave anet charge of 0.500 μC ?