eight identical point charges of Q coul each are placed at the corners of a cube whose sides have a length of 10cm.[a] find the electric field at the center of the cube. [b]find the electric field at the center of the face of a cube.[c] find the field at the center of a cube if one of the corner charge is removed.
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Answer:
Solution: Answer: Zero ; (1.2×10
12
q)NC
−1
towards the corner without chargeSolution: Length of each side a=0.1m=10cm
∴ distance of the center of the cube from each corner,
r=
2
a
3
=
2
10
3
=5
3
cm
=5
3
×10
−2
m.
When identical point charges +q each are at the eight corners of the cube, net field intensity at the center is zero (cancelling out in four pairs). When one of the corner charges is removed, three pairs of E values cancel. Due to charge on seventh corner,
E=
4π∈
0
1
r
2
q×1
=9×10
9
(5
3
×10
−2
)
2
q
=(1.2×10
12
q)NC
−1
It is towards the corner without charge directed radially away from +q.
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