An infinite conductive plate has charge density o, when it is brought in from infinity and placed between x=0 and x=1 m (it is 1 m thick, just a small portion is pictured below). A second infinite conductive plate has charge density o, when it is brought in from infinity and placed between x=5 and x=6 m. Additional information below. a) Find the electric field at the following locations: (i) (-6, 0) (ii) (-4, 2) (iii) (0.5, 0) (iv) (2, 0) (v) (5.5, 0) (vi) (7, 0) b) Find the electric potential at the following locations: (i) (-6, 0) (ii) (-4, 2) (iii) (0.5, 0) (iv) (2, 0) (v) (5.5, 0) (vi) (7,0) Additional Information: o, = 3x10-10 C/m² 02 = -4x10-10 C/m² V=0 at x=1 -5 -3 -1 0 2 4 8 10 x (m)
An infinite conductive plate has charge density o, when it is brought in from infinity and placed between x=0 and x=1 m (it is 1 m thick, just a small portion is pictured below). A second infinite conductive plate has charge density o, when it is brought in from infinity and placed between x=5 and x=6 m. Additional information below. a) Find the electric field at the following locations: (i) (-6, 0) (ii) (-4, 2) (iii) (0.5, 0) (iv) (2, 0) (v) (5.5, 0) (vi) (7, 0) b) Find the electric potential at the following locations: (i) (-6, 0) (ii) (-4, 2) (iii) (0.5, 0) (iv) (2, 0) (v) (5.5, 0) (vi) (7,0) Additional Information: o, = 3x10-10 C/m² 02 = -4x10-10 C/m² V=0 at x=1 -5 -3 -1 0 2 4 8 10 x (m)
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Transcribed Image Text:### Conductive Plates and Electric Fields
**Problem Statement:**
An infinite conductive plate with charge density \(\sigma_1\) is brought from infinity and placed between \(x = 0\) and \(x = 1 \, \text{m}\). A second infinite conductive plate with charge density \(\sigma_2\) is brought from infinity and placed between \(x = 5\) and \(x = 6 \, \text{m}\).
**Tasks:**
a) Find the electric field at the following locations:
- (i) (-6, 0)
- (ii) (-4, 2)
- (iii) (0.5, 0)
- (iv) (2, 0)
- (v) (5.5, 0)
- (vi) (7, 0)
b) Find the electric potential at the following locations:
- (i) (-6, 0)
- (ii) (-4, 2)
- (iii) (0.5, 0)
- (iv) (2, 0)
- (v) (5.5, 0)
- (vi) (7, 0)
**Additional Information:**
- \(\sigma_1 = 3 \times 10^{-10} \, \text{C/m}^2\)
- \(\sigma_2 = -4 \times 10^{-10} \, \text{C/m}^2\)
- \(V = 0 \, \text{at} \, x = 1\)
**Diagram Explanation:**
- The diagram includes a number line representing the \(x\)-axis in meters.
- Two shaded regions indicate the positions of the two conductive plates:
- The first plate is between \(x = 0\) and \(x = 1\).
- The second plate is between \(x = 5\) and \(x = 6\).
These plates influence the electric field and potential at the specified points, which are located at different positions along the number line.
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