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Of the charge q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. both spheres can be treated as particles. for what value of q/q>0.5 will the electrostatic force between the two parts have 1/4 of the maximum possible value?

Respuesta :

When two sphere will have maximum force then the charge will be equally divided among them

so here we can say

[tex]F = \frac{kq_1q_2}{r^2}[/tex]

here for maximum force

[tex]q_1 = q_2 = \frac{q}{2}[/tex]

now we have

[tex]F_{max} = \frac{kq^2}{4r^2}[/tex]

now we have to find the charge transferred so that force is 1/4 times the maximum force

[tex]\frac{1}{4}(\frac{kq^2}{4r^2}) = \frac{k(q_1)(q-q_1)}{r^2}[/tex]

here in above equation q1 is charge that is transferred

[tex]\frac{q^2}{16} = q q_1 - q_1^2[/tex]

[tex]q_1^2 - q q_1 + \frac{q^2}{16} = 0[/tex]

now by solving above equation we have

[tex]q_1 = \frac{q \pm \sqrt{q^2 - q^2/4}}{2}[/tex]

[tex]q_1 = 0.067q[/tex]

so we will have

[tex]\frac{q_1}{q} = 0.067[/tex]

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