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If D = 2rur C/m2, the total electric flux leaving the surface of the cube, 0 < x , y, z < 0.4 is
- a)0.32
- b)0.34
- c)0.38
- d)0.36
Correct answer is option 'C'. Can you explain this answer?
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If D = 2rur C/m2, the total electric flux leaving the surface of the c...
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If D = 2rur C/m2, the total electric flux leaving the surface of the c...
To find the total electric flux leaving the surface of the cube, we need to calculate the flux through each face of the cube and then sum them up.
Let's consider each face of the cube separately and calculate the flux through each face.
Face 1: This face is perpendicular to the x-axis. The electric field passing through this face is given by E1 = D * A1, where A1 is the area of face 1. Since the area of a square face is given by A1 = (side)^2, we have A1 = (0.4)^2 = 0.16 m^2. Therefore, E1 = D * A1 = 2ru * 0.16 C.
Face 2: This face is perpendicular to the y-axis. The electric field passing through this face is given by E2 = D * A2, where A2 is the area of face 2. Similar to face 1, we have A2 = (0.4)^2 = 0.16 m^2. Therefore, E2 = D * A2 = 2ru * 0.16 C.
Face 3: This face is perpendicular to the z-axis. The electric field passing through this face is given by E3 = D * A3, where A3 is the area of face 3. Again, we have A3 = (0.4)^2 = 0.16 m^2. Therefore, E3 = D * A3 = 2ru * 0.16 C.
Face 4: This face is also perpendicular to the x-axis. The electric field passing through this face is given by E4 = D * A4, where A4 is the area of face 4. Similar to face 1 and face 4, we have A4 = (0.4)^2 = 0.16 m^2. Therefore, E4 = D * A4 = 2ru * 0.16 C.
Face 5: This face is also perpendicular to the y-axis. The electric field passing through this face is given by E5 = D * A5, where A5 is the area of face 5. Similar to face 2 and face 5, we have A5 = (0.4)^2 = 0.16 m^2. Therefore, E5 = D * A5 = 2ru * 0.16 C.
Face 6: This face is also perpendicular to the z-axis. The electric field passing through this face is given by E6 = D * A6, where A6 is the area of face 6. Similar to face 3 and face 6, we have A6 = (0.4)^2 = 0.16 m^2. Therefore, E6 = D * A6 = 2ru * 0.16 C.
Now, to find the total flux, we sum up the electric fields passing through each face:
Total Flux = E1 + E2 + E3 + E4 + E5 + E6
= 2ru * 0.16 C + 2ru * 0.16 C + 2ru * 0.16 C + 2ru * 0.16 C + 2ru * 0.16 C + 2ru * 0.16
Let's consider each face of the cube separately and calculate the flux through each face.
Face 1: This face is perpendicular to the x-axis. The electric field passing through this face is given by E1 = D * A1, where A1 is the area of face 1. Since the area of a square face is given by A1 = (side)^2, we have A1 = (0.4)^2 = 0.16 m^2. Therefore, E1 = D * A1 = 2ru * 0.16 C.
Face 2: This face is perpendicular to the y-axis. The electric field passing through this face is given by E2 = D * A2, where A2 is the area of face 2. Similar to face 1, we have A2 = (0.4)^2 = 0.16 m^2. Therefore, E2 = D * A2 = 2ru * 0.16 C.
Face 3: This face is perpendicular to the z-axis. The electric field passing through this face is given by E3 = D * A3, where A3 is the area of face 3. Again, we have A3 = (0.4)^2 = 0.16 m^2. Therefore, E3 = D * A3 = 2ru * 0.16 C.
Face 4: This face is also perpendicular to the x-axis. The electric field passing through this face is given by E4 = D * A4, where A4 is the area of face 4. Similar to face 1 and face 4, we have A4 = (0.4)^2 = 0.16 m^2. Therefore, E4 = D * A4 = 2ru * 0.16 C.
Face 5: This face is also perpendicular to the y-axis. The electric field passing through this face is given by E5 = D * A5, where A5 is the area of face 5. Similar to face 2 and face 5, we have A5 = (0.4)^2 = 0.16 m^2. Therefore, E5 = D * A5 = 2ru * 0.16 C.
Face 6: This face is also perpendicular to the z-axis. The electric field passing through this face is given by E6 = D * A6, where A6 is the area of face 6. Similar to face 3 and face 6, we have A6 = (0.4)^2 = 0.16 m^2. Therefore, E6 = D * A6 = 2ru * 0.16 C.
Now, to find the total flux, we sum up the electric fields passing through each face:
Total Flux = E1 + E2 + E3 + E4 + E5 + E6
= 2ru * 0.16 C + 2ru * 0.16 C + 2ru * 0.16 C + 2ru * 0.16 C + 2ru * 0.16 C + 2ru * 0.16
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If D = 2rur C/m2, the total electric flux leaving the surface of the cube, 0 <x , y, z < 0.4 isa)0.32b)0.34c)0.38d)0.36Correct answer is option 'C'. Can you explain this answer?
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