Electrostatics 5 Question 15

17. A charged particle is free to move in an electric field. Will it always move along an electric line of force?

(1979)

(d) E1E2=(K1+K2+K3)(K2K3+K3K1+K1K2)9K1K2K3

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Solution:

  1. Let’s consider a strip of thickness ’ dx ’ at a distance of ’ x ’ from the left end as shown in the figure. From the figure, ABC and ADE are similar triangles,

yx=day=dax

We know that, the capacitance of parallel plate capacitor,

C=ε0AdC1=ε0(adx)(dy) and C2=Kε0(adx)y

Here, two capacitor are placed in series with variable thickness, therefore

Ceq=C1C2C1+C2Ceq=Kε0adxKd+(1K)y

Now, integrate it from 0 to a

C=0aKε0adxKd+(1K)y

Using Eq. (i), y=dax, we get

C=ε0a0adxd+1K1daxC=ε0a1KKdaln1KC=ε0a2KlnK(K1)d



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