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NCERT Class XII Chapter
Electric Charges and Fields
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Question : 27 of 34
Marks: +1, -0
In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 10510^5 N C−1C^{-1} per metre. What are the force and torque experienced by a system having atotal dipole moment equal to 10−710^{-7} C m in the negative z- direction?
Solution:  
As electric field increases in positive z-direction from A to B, So
EBE_B = EA+dEdRE_A + \frac{dE}{dR} . 2a
So, the net force on the electric dipole in electric field is
FnetF_{\text{net}} = FB−FAF_B-F_A = q (EB−EA)(E_B-E_A) or FnetF_{\text{net}} = q [EA+dEdr⋅2a−EA]\left[E_A + \frac{dE}{dr} \cdot 2a - E_A\right]
FnetF_{\text{net}} = q . 2adEdr2a \frac{dE}{dr} = p . dEdr\frac{dE}{dr} or FnetF_{\text{net}} = 10−7×10510^{-7} \times 10^5 or FnetF_{\text{net}} = 10−210^{-2} N directed in direction of FB→\overset{\rightarrow}{F_B} i.e., from B to A or along –z direction.
As the two forces on charges of electric dipole are collinear and opposite, so net torque on it is equal to zero.
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