# Two equal and opposite charges 4×10^{-8}C are placed 2×10^{-2} cm away, from a dipole. If this dipole is placed in an external electric field of 4×10^8NC^{-1}

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Two equal and opposite charges $$4×10^{-8}C$$ are placed $$2×10^{-2}$$ cm away, from a dipole. If this dipole is placed in an external electric field of $$4×10^8NC^{-1}$$, the value of maximum torque and the work done in rotating it through 180o will be

(A) $$64×10^{-4}Nm$$ and $$64×10^{-4}J$$

(B) $$32×10^{-4}Nm$$ and $$32×10^{-4}J$$

(C) $$64×10^{-4}Nm$$ and $$32×10^{-4}J$$

(D) $$32×10^{-4}Nm$$ and $$64×10^{-4}J$$

The correct answer of this question is (D).

Solution :

Maximum torque is given by

$$\iota_{max} = pE$$  ($$Sin \theta = 1$$)

$$=(q2a)E$$  ($$p=q×2a$$)

$$=(4×10^{-8}×2×10^{-4})×4×10^8$$

$$=32×10^{-4}Nm$$

If $$\theta = 180^o,$$ then

$$= W=pE(1-cos 180^o)$$

$$=pE[1-(-1)]=2pE$$

$$=2×32×10^{-4}$$

$$=64×10^{-4}J$$