An electric field is given by E = zy 2 a x + 2xyz a y + xy 2 a z
| An electric field is given by E = zy2ax + 2xyz ay+ xy2az V/m, an incremental path is represented by ΔL = -3ax + 5ay – 2az μm. Find the work done in moving 4 μC charge along the incremental path if the location of the path is at point P(1, 1, 1).
A. 20 pJ
B. 40 pJ
C. -40 pJ
D. -20 pJ
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Right Answer is: D
SOLUTION
Concept:
Work done for an incremental path is defined as
W = –q × E × ΔL
Calculation:
E̅ = zy2 ax + 2xyzay + xy2 az V/m
ΔL = -3ax + 5ay – 2az μm
q = 4 μC
Differential work done by an external source in moving q charge for ΔL distance is for E (1, 1, 1) = 1ax + 2ay + az V/m
dw = -q × E × ΔL
dw = -4 × 10-6 × (1ax + 2ay + az) × (-3ax + 5ay – 2az)μ
= -4 × 10-12 × (-3 + 10 - 2)
= -20 × 10-12 J
= -20 pJ