Question 46. Two charges of -4 \mu C and +4 \mu C are placed at the points A(1,0,4) m and B(2,-1,5) m located in an electric field \overrightarrow{E}=0.20 \hat{i} V / cm. The magnitude of the torque acting on the dipole is 8 \sqrt{\alpha} \times 10^{-5} Nm, Where \alpha= ____ .
Answer (2.00)
Explanation:
(1, 0, 4)
( 2,-1,5 )
4 \mu C \vec{\tau}=\overrightarrow{p} \times \overrightarrow{E} \overrightarrow{p}=q \vec{\ell} \overrightarrow{E}=0.2 \frac{~V}{~cm}=20 \frac{~V}{~m} \overrightarrow{p}=4 \times(\hat{i}-\hat{j}+\hat{k}) =(4 \hat{i}-4 \hat{j}+4 \hat{k}) \mu C-m \vec{\tau}=(4 \hat{i}-4 \hat{j}+4 \hat{k}) \times(20 \hat{i}) \times 10^{-6} Nm =(8 \hat{k}+8 \hat{j}) \times 10^{-5}=8 \sqrt{2} \times 10^{-5}