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- A net flux of 1.0104 N ? m2/C passes inward through the surface of a sphere of radius 5 cm (a) How much charge is inside the sphere? (b) How precisely can we determine the location of the charge from this information?Consider a uranium nucleus to be sphere of radius R=7.41015 m with a charge of 92e distributed uniformly throughout its volume. (a) is the electric force exerted on an electron when it is 3.01015 m from the center of the nucleus? (b) What is the acceleration of the electron at this point?A point charge q=5.01012 C is placed at the center of a spherical conducting shell of inner radius 3.5 cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is the charge density on the inner surface of the shell? (b) What is the charge density on the outer surface of the shell? (c) What is the net charge on the conductor?
- (a) Calculate the electric flux through the open hemispherical surface due to the electric field E =E0k (see below). (b) If the hemisphere is rotated by 90( around the what is the flux through it?Consider a uniform electric field ?⃗⃗=2kNC ?̂. (a) What is the flux of this field through a square of side 10 cm in a plane parallel to the yz-plane? (b) What is the flux through the same square if the normal to its plane makes a 30º angle with the x-axis?A non-uniformly charged semicircle of radius R=31.4 cm lies in the xy plane, centered at the origin, as shown. The charge density varies as the angle θ (in radians) according to λ=4.15θ, where λ has units of μC. a) What is the total charge on the semicircle? b) What is the y component of the electric field at the origin?
- A solid conductor carries a net positive charge −?. There is a hollow cavity within theconductor, at whose center is a negative point charge −?. What is the charge on:i. The inner surface of the conductor’s cavity? ii. The outer surface of the conductor?Consider a positive point charge Q which is at rest at the center of uncharged spherical conducting shell as shown in fig. How electric field E will behave (i) if r is less than the inner radius of the shell, (ii) inside the shell, and (iii) outside the shell? (iv) Does the shell affect the field due to Q alone? (v) Does the charge Q affect the shell?a loaded thin rod is bent into a semicircle of radius as shown in the figure. Charge density at a point on the rod, o the angle between the position vector of the point and the vertical c R λ = Acos(θ) : It is bound by the os expression. At the center of the semicircle (point O) what is the electric field?
- A thick, conducting, spherical shell of inner radius a and outer radius b carries an excess charge of −2Q. At the center of the spherical shell, a point charge −Q is placed. A. How is the charge −2Q distributed on the think spherical shell? (Just give an answer.) i. How much charge is on the surface of radius a ii. How much charge is on the surface of radius b B. What is the direction of the electric field (radially inward, radially outward or zero) in each of the following regions. (Just give an answer in the table provided.) r < a a <r r> bA point charge -4nC is at the center of a Gaussian sphere of radius to 0.35m. (a) What is the electric field at all points on the surface of the sphere? (b) What is the flux of the electric field through the surface of the sphere? (c) What is the electric flux through the surface of the sphere if the point charge is moved from the center to another location inside the Gaussian sphere?Find the electric field at a height z above the center of a square sheet (side a)carrying a uniform surface charge u.check your result for the limiting cases a~oo and z>>a