The capacitance of a spherical condenser is $$1$$ μF. If the spacing between the two spheres is $$1$$ mm, then the radius of the outer sphere is

Question

The capacitance of a spherical condenser is $$1$$ μF. If the spacing between the two spheres is $$1$$ mm, then the radius of the outer sphere is

Infinity Learn · Accepted Answer

Given : (b$$−$$a)=1$$×$$10$$−$$3m$$         ….$$(i)and$$ $$C=4$$πε$$0abb$$−$$a=1$$×$$10$$−$$6$$⇒$$1$$×$$10$$−$$6=19$$×$$109ab10$$−$$3$$⇒$$ab=9$$                                  ….$$(ii)From$$ equations $$(i) and (ii) b−$$9b=11000$$⇒$$1000b2$$−b−$$9000=0$$⇒$$b=1$$±$$($$−$$1)2$$−$$4(1000)($$−$$9000)2$$×$$1000$$  $${Solving$$ of quadratic $$equation}$$⇒$$b=1$$±$$36$$×$$1062000$$≈$$36$$×$$1062000=3m$$.

The capacitance of a spherical condenser is $1 μF$ . If the spacing between the two spheres is 1 mm, then the radius of the outer sphere is

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The capacitance of a spherical condenser is 1 μF. If the spacing between the two spheres is 1 mm, then the radius of the outer sphere is

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The capacitance of a spherical condenser is $1 μF$ . If the spacing between the two spheres is 1 mm, then the radius of the outer sphere is