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Question: An electric dipole consists of two opposite charges each of magnitude 2μC separated by a distance of...

An electric dipole consists of two opposite charges each of magnitude 2μC separated by a distance of 1cm. The dipole is placed in an external field of 103 N/C. The maximum torque on the dipole is
(A) 1×10−5Nm1 \times {10^{ - 5}}Nm
(B) 2×10−5Nm2 \times {10^{ - 5}}Nm
(C) 0.5×10−5Nm0.5 \times {10^{ - 5}}Nm
(D) Zero

Explanation

Solution

Hint
As, we know that the dipole moment is the product of charge and distance between the charges i.e. P=q×lP = q \times l, now the relation between torques and electric field and dipole moment is τ=P×E=PEsin⁡θ\tau = P \times E = PE\sin \theta , for maximum torque sin⁡θ=1\sin \theta = 1, after substituting the values, we get the maximum torque.

Complete step by step answer
It is given that electric dipole consists of two opposite charges each of magnitude 2μC separated by a distance of 1cm then the dipole moment of the dipole is
P=q×lP = q \times l …………………………… (1)
It is given that, q=2×10−6Cq = 2 \times {10^{ - 6}}C and l=1cm=0.01ml = 1cm = 0.01m
Substituting the values in equation (1), we get
⇒P=2×10−6×0.01=2×10−8\Rightarrow P = 2 \times {10^{ - 6}} \times 0.01 = 2 \times {10^{ - 8}}
Now the dipole is placed between the electric field of 103 N/C. then the torque acting on the dipole is
τ=P×E=PEsin⁡θ\tau = P \times E = PE\sin \theta …………………………. (2)
Here, θ is the angle between the electric field and dipole moment.
For maximum value of torque sin⁡θ=1\sin \theta = 1
Substitute the values in equation (2), we get
⇒τ=PE\Rightarrow \tau = PE
⇒τ=2×10−8×103\Rightarrow \tau = 2 \times {10^{ - 8}} \times {10^3}
⇒τ=2×10−5Nm\Rightarrow \tau = 2 \times {10^{ - 5}}Nm
This is the required value of maximum torque.
Hence, option (B) is correct.

Note
An arrangement of two equal and opposite charges separated by a finite distance is called an electric dipole. Electric dipole moment of an electric dipole is defined as the product of either of its charges and the length of the dipole. It is a vector quantity and is represented by P. In the above question care must be taken in choosing the appropriate units. As we want torque in Nm so while finding the dipole moment the distance must be converted in meters from centi-meter.