### Two Infinite, Very Thin Flat Sheets of Insulating MaterialTwo infinite, very thin, and flat sheets of insulating material carry an electric charge \( \sigma > 0 \) per unit area. The charge density is homogeneous. Sheet 1 lies at \( y = 0 \), and sheet 2 at \( y = d \).The electric fields generated by the sheets independently are:\[\mathbf{E_1} = \begin{cases} \frac{\sigma}{2\varepsilon_0} \hat{\mathbf{j}} & \text{for } y > 0 \\ -\frac{\sigma}{2\varepsilon_0} \hat{\mathbf{j}} & \text{for } y < 0 \end{cases}\]\[\mathbf{E_2} = \begin{cases} \frac{\sigma}{2\varepsilon_0} \hat{\mathbf{j}} & \text{for } y > d \\ -\frac{\sigma}{2\varepsilon_0} \hat{\mathbf{j}} & \text{for } y < d \end{cases}\]### Tasks1. **Sketch the System**: Draw the system of two sheets, and include the coordinate system.2. **Compute the Electric Field Vector using Superposition**: - Use the principle of superposition, \( \mathbf{E} = \mathbf{E_1} + \mathbf{E_2} \), to find the electric field vector \( \mathbf{E} \) generated by the two sheets: - (a) for \( y < 0 \) - (b) for \( 0 < y < d \) - (c) for \( d < y \)3. **Plot Electric Field Components**: Plot \( E_x \), \( E_y \), \( E_z \) and \( |\mathbf{E}| = \sqrt{E_x^2 + E_y^2 + E_z^2} \) as a function of \( y \). This exercise explores the properties of electric fields in the presence of charged flat sheets and applies the superposition principle to calculate the net field.

Two infinite, very thin and flat sheets of insulating material carry electric charge o > 0 per unit area. The charge density is homogeneous. Sheet 1 lays d. The electric fields generated by the sheets at y 0, and sheet 2 at y independently, that is, when the other sheet is absent, are E, = {3 {. - for y > d 2€0 i for y >0 (1) 2€0 E2 for y <0 ' 2€0 for y < d 2€0* 1. Make a sketch of the system of two sheets, including the coordinate system. 2. Use the principle of superposition, E = E1+E2, to compute the electric field vector E generated by the two sheets (a) for y < 0, (b) for 0 < y < d, (c) and for d < y. 3. Plot Eg, Ey, E, and |E| = /E + E; + E? as a function of y.

Two infinite, very thin and flat sheets of insulating material carry electric charge o > 0 per unit area. The charge density is homogeneous. Sheet 1 lays d. The electric fields generated by the sheets at y 0, and sheet 2 at y independently, that is, when the other sheet is absent, are E, = {3 {. - for y > d 2€0 i for y >0 (1) 2€0 E2 for y <0 ' 2€0 for y < d 2€0* 1. Make a sketch of the system of two sheets, including the coordinate system. 2. Use the principle of superposition, E = E1+E2, to compute the electric field vector E generated by the two sheets (a) for y < 0, (b) for 0 < y < d, (c) and for d < y. 3. Plot Eg, Ey, E, and |E| = /E + E; + E? as a function of y.