Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Electrical resistivity and conductivity wikipedia , lookup
Magnetic monopole wikipedia , lookup
Electromagnetism wikipedia , lookup
Speed of gravity wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Maxwell's equations wikipedia , lookup
Field (physics) wikipedia , lookup
Lorentz force wikipedia , lookup
PHYS 196 Home Work 3A 1. A thin rod carrying electric charge lies on the x-axis, with one end at the origin, and another at the point x 2 . The linear charge density on the rod is given by x C x3 3x 2 . Find (1) the total charge q carried by the rod in terms of C and (2) the x-component of the electric field E x at the origin in terms of q . 2. A thin rod carrying electric charge lies on the x-axis, with one end at the origin, and another at the point x 1 . The linear charge density on the rod is given by x C x3 3x 2 . Find (1) the total charge q carried by the rod in terms of C and (2) the x-component of the electric field E x at the point x 1 in terms of q . (Hint: factorize x ) 3. A thin rod carrying electric charge lies on the x-axis, with one end at the origin, and another at the point x a . The linear charge density on the rod is given by x Ax . Find (1) the total charge q carried by the rod in terms of A and a and (2) the x-component of the electric field E x at the point x 2a in terms of q and a . 4. A 90 arc of a circle of radius a is placed in the first quadrant of the x-y plane with its center at the origin. It carries a uniform charge distribution of linear density . Find the x and y components of the electric field at the origin. Hence find the magnitude and direction of the electric field. 5. A 270 arc of a circle of radius a is placed on the x-y plane, occupying the second, third and fourth quadrants, with its center at the origin. It carries a uniform charge distribution of linear density . Find the magnitude and direction of the electric field at the origin. (Hint: use the result from the previous problem.) 6. A thin wire of length 20cm carries a total charge of 24nC uniformly distributed over its length. Find the electric field at a point 6.0mm from the wire. (The distance of the point is so small the wire can be considered infinite in length.) 7. The diagram shows two parallel infinite line charges (charge density C / m ) a distance a apart. Find the magnitude of the electric field at the point P, which is on a plane perpendicular to the lines and is at distance a from one of the lines. a a 90º P 8. A 25cmx25cm square sheet carries a total charge of 40nC uniformly distributed over its area. Find the electric field at a point 3.0mm from the sheet. Find also the force on a 6.0nC charge placed at the point. (The point is so close to the sheet that the latter can be considered infinite.) 1 9. The diagram shows two parallel infinite sheet charges with surface charge densities and 3 respectively. Find the electric fields in the regions A, B and C. -σ -3σ A C \ B 10. A ring of radius a carrying a total charge q lies on the x-y plane with center at the origin. Find the direction and magnitude of the electric field at a point (0,0,z) on the z-axis. Find the value of z where this electric field is maximum. 11. A line charge of linear density extends to infinity from a perpendicular plane as shown. A point P on the plane is at a distance r from the point of intersection of the line and the plane. Use integration to find the components of the electric field at P parallel and perpendicular to the line. r P 12. (hard) A hemispherical shell of radius a carries a uniform surface charge density . Use integration to find the electric field at the center. (Hint: divide the hemisphere into thin rings using planes perpendicular to the axis, and use the formula for electric field due to the rings and integrate) Answers: 2kq 3 3C 10kq , 2. 4 3 2 Aa 2kq , (1 ln 2) 3. 2 a2 1. 12C , 8. 3.6 104 N / C 0.22mN 9. 0 , 10. a 2 0 , 0 , kqz 2 z 2 32 , 2k r 135 with x axis 11. k r k r 5. 2k r 45 with 6. 3.6 105 N / C k 7. 10 a x axis 12. k 4. 2 a 2