Cartesian co-ordinates in spherical co-ordinates

Question

1) Explain the source of electric field and magnetic fields in detail.

2) What do you mean by a scalar quantity?

3) What do you mean by a vector quantity?

4) Explain vector product of two vectors in detail.

5) Determine the dot product of vectors A and B if A = 2a_x-3a_y+4a_z, B = -a_x+2a_y+2a_z.

6) Write an expression for x,y,z in terms of spherical co-ordinates r, θ and ?.

7) Signify point P (0, 1, 1) m given in Cartesian co-ordinates in spherical co-ordinates.

8) Write down three co ordinate systems.

9) Express value of differential volume in rectangular and cylindrical co-ordinate systems.

10) Write down an expression for differential length in cylindrical and spherical co- ordinates.