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Let E = (-200ax + 30ay + 70az) cos 10t V/m at point 'P which lies on the surface of a perfect conductor P (3, -4,1). If a material adjacent to the conductor has ∈r = 5, μf = 0, σ = 0, then surface charge density on the conductor surface at P
  • a)
    ±5.2 cos2 10t 
  • b)
    ± 3.48 cos 102t
  • c)
    ± 5.2 cos 104t
  • d)
    ± 3.48 cos 104t
Correct answer is option 'D'. Can you explain this answer?
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Let E = (-200ax+ 30ay + 70az) cos 104t V/m at point 'P which lies ...
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Let E = (-200ax+ 30ay + 70az) cos 104t V/m at point 'P which lies ...
Given Information:
- Electric field E = (-200ax+ 30ay + 70az) cos 104t V/m at point P (3, -4,1)
- Point P lies on the surface of a perfect conductor
- Material adjacent to the conductor has r = 5, f = 0, θ = 0

Surface Charge Density Calculation:
- The surface charge density on a perfect conductor is given by σ = n * E
- Where n is the unit normal vector to the surface

Unit Normal Vector Calculation:
- The unit normal vector n at point P is given by n = (n_x, n_y, n_z) = (5, 0, 0) (due to the material properties)
- Therefore, n = 5ax

Electric Field at Point P:
- Substitute the values of n and E at point P in the formula for surface charge density
- E = (-200ax+ 30ay + 70az) cos 104t V/m
- n = 5ax
- σ = n * E = 5 * (-200ax+ 30ay + 70az) cos 104t
- σ = -1000ax cos 104t + 150ay cos 104t + 350az cos 104t

Comparing with Options:
- Comparing the calculated surface charge density with the given options
- Option 'D' matches with the calculated surface charge density: 3.48 cos 104t
Therefore, the correct answer is option 'D' - 3.48 cos 104t.
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Let E = (-200ax+ 30ay + 70az) cos 104t V/m at point 'P which lies on the surface of a perfect conductor P (3, -4,1). If a material adjacent to the conductor has ∈r = 5, μf = 0, σ = 0, then surface charge density on the conductor surface at Pa)±5.2 cos2 10tb)± 3.48 cos 102tc)± 5.2 cos 104td)± 3.48 cos 104tCorrect answer is option 'D'. Can you explain this answer?
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