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
Density of states wikipedia , lookup
Four-vector wikipedia , lookup
Speed of gravity wikipedia , lookup
Noether's theorem wikipedia , lookup
Magnetic monopole wikipedia , lookup
Maxwell's equations wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Field (physics) wikipedia , lookup
Centripetal force wikipedia , lookup
Lorentz force wikipedia , lookup
Assignment problems Chapter-1 1. In the Cartesian coordinate system; verify the following relations for a scalar function V and a vector function A (a) V 0 (b) A 0 (c) (VA) V A V A 2. An electric field expressed in spherical polar coordinates is given by E 9 aˆr . r2 Determine E and E y at a point P (1, 2, 2) . 3. Evaluate S sin aˆr dS over the surface of a sphere of radius r0 centered at the r02 origin. 4. Find the divergence of the radial vector field given by f r aˆr r n . 5. A vector function is defined by A xy 2 aˆ x yx 2 aˆ y . Find contour shown in the figure……... Evaluate verify that A dl A ds . Fig……. A dl around the A ds over the shaded area and Chapter 2 1. A charged ring of radius d carrying a charge of L C/m lies in the x-y plane with its centre at the origin and a charge Q C is placed at the point (0, 0, 2d ) . Determine L in terms of Q and d so that a test charge placed at (0, 0, 2d ) does not experience any force. 2. A semicircular ring of radius a lies in the free space and carries a charge density L C/m. Find the electric field at the centre of the semicircle. 3. Consider a uniform sphere of charge with charge density o and radius b, centered at the origin. Find the electric field at a distance r from the origin for the two cases: r<b and r>b. Sketch the strength of the electric filed as function of r. 4. A spherical charge distribution is given by 0 (a 2 r 2 ), v 0, ra ra a is the radius of the sphere. Find the following: (i) (ii) The total charge. E for r a and r a . The value of r where the E becomes maximum. (iii) 5. With reference to the Fig. ___ determine the potential and field at the point P (0, 0, h) if the shaded region contains uniform charge density s /m2. 6. A capacitor consists of two coaxial metallic cylinders of length L , radius of the inner conductor a and that of outer conductor b . A dielectric material having dielectric constant r 3 2 / , where is the radius, fills the space between the conductors. Determine the capacitance of the capacitor. 7. Determine whether the functions given below satisfy Laplace’s equation 1 (i) V ( x, y , z ) (ii) V ( , , z ) z sin 2 x2 y 2 z 2 8. A point charge Q is placed at a distance d from a large grounded conducting plane. Let us consider a region on the grounded plane bounded between two concentric circles of radii d and 2d respectively. The circles are placed vertically below the point charge in such a way that their centers are exactly below the point charge. If the region under consideration shows a total charge of 1 C , determine the charge Q .