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Electromagnetic Theory Preparation Questions 1. A sphere of radius 2 cm contains a volume charge density ?v given by ?v = 4cos²? (C/m²). Find the total charge Q contained in the sphere. 2. Given point P? = (3,-4,3) and vector A = a?x2 - a?y3 + a?z4 defined in Cartesian coordinates, express P? and A in cylindrical coordinates and evaluate A at P?. 3. Two point charges with q? = 2 x 10??C and q? = -4 x 10??C are located in free space at points with Cartesian coordinates (1,3,-1) and (-3,1,-2), respectively. Find a. the electric field E at (3,1,-2) b. the force on a 8 x 10??C charge located at that point. 4. Obtain an expression for E due to an infinitely long line with uniform charge density ?l that resides along the z axis in free space. 5. In a given region of space, the field E is given by E = a?xx² + a?yy² + a?zz². a. Compute the potential difference between points 1 and 2 in Figure following the direct path between them. b. Compute the potential difference by following the path ABCD between points 1 and 2. 6. A charge Q is distributed uniformly over the wall of a circular tube of radius b and height h. Determine V and E on its axis a. At a point outside tube, then b. At a point inside tube. 7. Consider the planar sheet of charge of infinite extent located in the xy plane (z = 0). The surface charge density is given as ?s. Determine V and E. 8. A charge Q is distributed uniformly over an L x L square plate. Determine V and E at a point on the axis perpendicular to the plate and through its center.

Electromagnetic Theory Preparation Questions

1. A sphere of radius 2 cm contains a volume charge density ?v given by ?v = 4cos²? (C/m²). Find the total charge Q contained in the sphere.

2. Given point P? = (3,-4,3) and vector A = a?x2 - a?y3 + a?z4 defined in Cartesian coordinates, express P? and A in cylindrical coordinates and evaluate A at P?.

3. Two point charges with q? = 2 x 10??C and q? = -4 x 10??C are located in free space at points with Cartesian coordinates (1,3,-1) and (-3,1,-2), respectively. Find
a. the electric field E at (3,1,-2)
b. the force on a 8 x 10??C charge located at that point.

4. Obtain an expression for E due to an infinitely long line with uniform charge density ?l that resides along the z axis in free space.

5. In a given region of space, the field E is given by E = a?xx² + a?yy² + a?zz².
a. Compute the potential difference between points 1 and 2 in Figure following the direct path between them.
b. Compute the potential difference by following the path ABCD between points 1 and 2.

6. A charge Q is distributed uniformly over the wall of a circular tube of radius b and height h. Determine V and E on its axis
a. At a point outside tube, then
b. At a point inside tube.

7. Consider the planar sheet of charge of infinite extent located in the xy plane (z = 0). The surface charge density is given as ?s. Determine V and E.

8. A charge Q is distributed uniformly over an L x L square plate. Determine V and E at a point on the axis perpendicular to the plate and through its center.

Electromagnetic Theory Preparation Questions

1. A sphere of radius 2 cm contains a volume charge density ?v given by ?v = 4cos²? (C/m²). Find the total charge Q contained in the sphere.

2. Given point P? = (3,-4,3) and vector A = a?x2 - a?y3 + a?z4 defined in Cartesian coordinates, express P? and A in cylindrical coordinates and evaluate A at P?.

3. Two point charges with q? = 2 x 10??C and q? = -4 x 10??C are located in free space at points with Cartesian coordinates (1,3,-1) and (-3,1,-2), respectively. Find
a. the electric field E at (3,1,-2)
b. the force on a 8 x 10??C charge located at that point.

4. Obtain an expression for E due to an infinitely long line with uniform charge density ?l that resides along the z axis in free space.

5. In a given region of space, the field E is given by E = a?xx² + a?yy² + a?zz².
a. Compute the potential difference between points 1 and 2 in Figure following the direct path between them.
b. Compute the potential difference by following the path ABCD between points 1 and 2.

6. A charge Q is distributed uniformly over the wall of a circular tube of radius b and height h. Determine V and E on its axis
a. At a point outside tube, then
b. At a point inside tube.

7. Consider the planar sheet of charge of infinite extent located in the xy plane (z = 0). The surface charge density is given as ?s. Determine V and E.

8. A charge Q is distributed uniformly over an L x L square plate. Determine V and E at a point on the axis perpendicular to the plate and through its center.

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