Problem 3: A cube is centered on the origin. Its sides are parallel to the x - y, the y x - z planes and have edges of length of L. It is immersed in an electric field given by E(x) = Eo (ax+2j+5k) z, and the У Refer to the figure. N\ X Part (a) Using only the symbols in the palette, enter an expression for the total electric flux through the cube. Part (b) Given L = 8.41 m, a = 1.09/m³, and Eo - E=0.000 V.m X Attempts Remain Part (c) If the electric field is = 71.8 V/m, what is the value, in volt meters, of the electric flux through the cube? E(z) = E(x² +23+15) with B 2.5/m². Given L = 8.41 m and E0 = 71.8 V/m, what is the value, in volt meters, of the electric flux through the cube? =

The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball's center and has magnitude 4.0102 N/C. How much charge is on the surface of the ball?

A closed surface with dimensions a = b 0.272 m and c = the figure. The electric field throughout the region is nonuniform and defined by E (a+ Br)î where r is in meters, a = 3 N/C, and 3 = 5 N/(C -m²). 0.4896 m is located as in E What is the magnitude of the net charge enclosed by the surface? Answer in units of C. A. to sh What is the sign of the charge enclosed in the surface? R 1. Cannot be determined 2. Negative 3. Positive

Figure 2 shows a nonconducting rod with a uniformly distributed charge Q. The rod forms a half-circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P, by what factor is the magnitude of the electric field at P multiplied?

An electric field of magnitude 5130 N/C is applied along the r axis. Calculate the electric flux through a rect- angular plane 0.375 m wide and 0.29 m long if the plane is parallel to the yz plane. Answer in units of N m/C. Calculate the electric flux through the same rectangle if it is parallel to the ry plane. Answer in units of N m/C. Calculate the electric Hux through the same rectangle if it now contains the y axis and its normal makes an angle of 55° with the r axis. m²/C. Answer in units of N m/C.

b y а 30° An object having the shape of a rectangular prism is placed in a uniform electric field with constant magnitude (E) as shown in the figure. As shown in the figure, the electric field has an angle of 30° to the right surface numbered with 1. What is the total electric flux in terms of Nm²/C through the top (2) and right (1) surfaces? (E=100 N/C; a=2m; b=4m; c=6m).

An infinite cylindrical conductor has an inner radius ra =57.9mm and an outer radius 70.4mm. The conductor has a linear charge density of A₁ =136. On the axis of the cylinder is an infinite line charge with linear charge density ₂ = -9€. Determine the electric field magnitude at the point r = 31.03mm (in) C O

Two rings of radius R-5 cm are 34 cm apart and concentric with a common vertical axis (figure below). Ring 1 carries a uniformly distributed charge Q₁ = 20 nC and ring 2 carries a uniformly distributed charge of Q₂ = -70 nC. T A Ring 2 Ring 1 1. Find the magnitude of the electric field E created by Ring 1 at point A, halfway between the two rings. E₁ = [N/C] What is the direction of the electric. 2. field E, created by Ring 1 at point A. Direction: + 3. Write the expression of the electric filed E₁ created by Ring 1 at point A. E₁ = [N/C] > [N/C] 7. If vector E₁ = [N/C] and vector Ē₂ = [N/C]. Find the net electric filed Enet at point A. Ēnet = [N/C] 8. If a charge q = 5 nC is placed at location A, what would be the force on this charge? Use the answer of question 7.

A positively charged cylinder has a uniform volume charge density. Height l is larger than its radius a (1»a). a P a. When Point P is very close to the surface of the cylinder (1>r>a), the electric field there can be derived by treating the cylinder as an = Eŝ. infinitely long one. Suppose that we already measure the electric field at P as charge density in terms of E and a (ŝ is the radial unit vector in the cylindrical coordinate system as defined in the Equation: now use the Gauss's law to find the volume cos o â + sin ø ŷ, - sin ø Âx + cos ø ŷ, î. b. Now we move the detector from Point P to Point Q, which is so far away from the cylinder (R>l>a), that the cylinder can be treated as a point. Based on result in Part (a), find out the electric field at Q (Note that OQ is in the x direction.)

An electric field of magnitude equal to 8200 N/C is applied along the y-axis. Calculate the electric flux through a square plane of side 1.5 ft if: a) The plane is parallel to the yz plane.b) The plane is parallel to the xz plane.