An electric dipole consists of two opposite charges each of magnitude 1×10^-6 C saperated by a distance 2cm. The dipole is placed in an external electric field of 10×10^5 N/C. The maximum torque on dipole is -
A. 0.2×10^-3 N-m
B. 1.0×10^-3 N-m
C. 2×10^-3 N-m
D. 4×10^-3 N-m
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Answer:
An electric dipole consist at two opposite charge each of magnitude =1μC=1×10
−6
C
distance =2cm
Exter field =10
5
N/C
maximum torque on the dipole =?
q=1×10
−6
C,2a=2cm
or, =0.02cm
∴ P=q×2a
=(1×10
−6
)×0.02
=2×10
−8
cm
Intensity of the external electric field, E=1.0×10
5
N/C
(i) Z
max
=pE=(2×10
−8
)(10×10
5
)=2×10
−3
N−m
(ii) Net work done in turning the dipole from 0
0
to 180
0
i.e W=∫
0
0
180
0
r
dθ=∫
0
0
180
0
pEsinθdθ
=pE[−cosθ]
0
0
180
0
=−pE(cos180
0
−cos0
0
)
=2pE
=2×(2×10
−8
)(1×10
5
)J
=4×10
−3
J
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