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Question

If the dielectric constant is K then, find the electric field at equator of dipole?

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Solution

If K e the dielectric constant, then electric field.

E1=14πε0Kq(r2+l2)andE2=14πε0Kq(r2+l2)

E=E1cosθ+E2cosθ

E=14πε0Kq(r2+I2)cosθ+14πε0Kq(r2+l2)cosθ

E=14πε0Kq(r2+l2)×2cosθ

cosθ=OAPA=OA(OP2+OA2)1/2=l(r2+l2)1/2

E=14πε0Kq(r2+l2)×2l(r2+l2)1/2=14πε0K×2ql(r2+l2)3/2

But 2ql=p= electric dipole moment

E=14πε0K×p(r2+l2)3/2

E=14πε0Kp(r2)3/2=14πε0Kpr3

Hence, electric field at the equator of dipole is E=14πε0Kpr3


1052950_1170207_ans_de68f55ef4bc4ce29f6f0aeb95a25172.png

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