Four charge particles each having charge $$Q=1$$ C are fixed at corners of base (at$$ A, B, C and $$D) of a square pyramid with slant length 'a' (AP=BP=DP=PC=a=2m),a charge $$-Q$$ is fixed at point P. A dipole with dipole moment $$p=$$ $$1$$ $$C-m$$ is placed at centre of base and perpendicular to its plane as shown in figure. If the force on dipole due to charge particles is Ω$$4$$πε$$0N$$. The value of Ω is $$_________$$.

Question

Four charge particles each having charge $$Q=1$$ C are fixed at corners of base (at$$ A, B, C and $$D) of a square pyramid with slant length 'a' (AP=BP=DP=PC=a=2m),a charge $$-Q$$ is fixed at point P. A dipole with dipole moment $$p=$$ $$1$$ $$C-m$$ is placed at centre of base and perpendicular to its plane as shown in figure. If the force on dipole due to charge particles is Ω$$4$$πε$$0N$$. The value of Ω is $$_________$$.

Infinity Learn · Accepted Answer

Charges at A, B, C and D are placed at equilateral position of dipole. Hence force on each of them due to $$dipoleF1=Qp4$$π∈$$0(a/2)3This$$ force is downward on charges. Hence force due to these charges on dipole is $$4F1$$ upwards.Force on dipole due to charge at P:$$F2=Q$$⋅$$2pQ4$$π∈$$0(a/2)2(upward)$$ Net force on dipole: $$F=4F1+F2=32Qp$$π∈$$0a3$$ upward  After substituting given values we get $$F=64$$πε$$0N$$.

Detailed Solution

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