I have two questions from my practice test and they are 1)Two charges are separa

Question

I have two questions from my practice test and they are


1)Two charges are separated by a distance d and exert a mutualattractive force of magnitude F on each other. In the chargesare moved loser so that they are separated by a distance of d/3,the magnitude of the new mutual force of attraction is  a)F/3 b)F/9 c)F d)3F e)9F

the answer is e but why?


2)A 15F capacitor is connected to a 50-V battery and fullycharged. The battery is removed and a slab of dielectric(K=5) that completely fils the space between the plates isinserted. The voltage (in V) acrosse the capacitor plateswill be   a)250 b)10 c)2.0  d).75   e)0.0

the answer here is b but i got a and i'm not sure how to achieveb.

Explanation / Answer

A) F = k Q1 Q2 / r2 1 / (d/3)2 = 9 * 1 / d2 so theforce is 9 times greater if the separation is reduced to 1/3 B) C = k C0 where k is the dielectricconstant and C0 the capacitance in air Then V = V0 / k   since the chargeremains the same and V = 10 Q = C V   increasing the capacitance by 5 decreasesthe voltage by 5 for constant Q 1 / (d/3)2 = 9 * 1 / d2 so theforce is 9 times greater if the separation is reduced to 1/3 B) C = k C0 where k is the dielectricconstant and C0 the capacitance in air Then V = V0 / k   since the chargeremains the same and V = 10 Q = C V   increasing the capacitance by 5 decreasesthe voltage by 5 for constant Q

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