1 - шар радиусом 2 см, 2 - шар радиусом 5 см
Потенциал заряженного металлического шара:
![\phi = \frac{kq}{R} \phi = \frac{kq}{R}](https://tex.z-dn.net/?f=%5Cphi%20%3D%20%5Cfrac%7Bkq%7D%7BR%7D)
После соприкосновения потенциалы шаров будут равными и суммарный заряд должен сохраниться:
![q_1+q_2=q'_1+q'_2 = Q;\\\phi_1=\phi_2;\\\frac{kq'_1}{R_1}=\frac{kq'_2}{R_2}; \frac{q'_1}{R_1}=\frac{q'_2}{R_2};\\\frac{q'_1}{R_1}=\frac{Q-q'_1}{R_2}; \\q'_1R_2=QR_1-q'_1R_1;\\q'_1=Q\frac{R_1}{R_1+R_2}; q'_2=Q-q'_1=Q\frac{R_2}{R_1+R_2}; q_1+q_2=q'_1+q'_2 = Q;\\\phi_1=\phi_2;\\\frac{kq'_1}{R_1}=\frac{kq'_2}{R_2}; \frac{q'_1}{R_1}=\frac{q'_2}{R_2};\\\frac{q'_1}{R_1}=\frac{Q-q'_1}{R_2}; \\q'_1R_2=QR_1-q'_1R_1;\\q'_1=Q\frac{R_1}{R_1+R_2}; q'_2=Q-q'_1=Q\frac{R_2}{R_1+R_2};](https://tex.z-dn.net/?f=q_1%2Bq_2%3Dq%27_1%2Bq%27_2%20%3D%20Q%3B%5C%5C%5Cphi_1%3D%5Cphi_2%3B%5C%5C%5Cfrac%7Bkq%27_1%7D%7BR_1%7D%3D%5Cfrac%7Bkq%27_2%7D%7BR_2%7D%3B%20%5Cfrac%7Bq%27_1%7D%7BR_1%7D%3D%5Cfrac%7Bq%27_2%7D%7BR_2%7D%3B%5C%5C%5Cfrac%7Bq%27_1%7D%7BR_1%7D%3D%5Cfrac%7BQ-q%27_1%7D%7BR_2%7D%3B%20%5C%5Cq%27_1R_2%3DQR_1-q%27_1R_1%3B%5C%5Cq%27_1%3DQ%5Cfrac%7BR_1%7D%7BR_1%2BR_2%7D%3B%20q%27_2%3DQ-q%27_1%3DQ%5Cfrac%7BR_2%7D%7BR_1%2BR_2%7D%3B)
q'1 = 3,5*10^(-9) * 2/7 = 1*10^(-9) Кл = 1 нКл;
q'2 = 3,5*10^(-9) * 5/7 = 2,5*10^(-9) Кл = 2,5 нКл.