A disk of radius a /4 having a uniformly distributed charge 6 C is placed in the x − y plane with its centre at ( − a /2 , 0 , 0). A rod of length a carrying a uniformly distributed charge 8C is place

Question

A disk of radius a /4 having a uniformly distributed charge 6 C is placed in the x − y plane with its centre at ( − a /2 , 0 , 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x=a/4 to x= 5a/4. Two point charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0) respectively. Consider a cubical surface formed by six surfaces x = ± a /2 , y = ± a /2 , z = ± a /2 . The electric flux through this cubical surface is ε 0 ​ xC ​ , then find x :-

TestHub · Accepted Answer

Only charge inside the cube x , y , z ∈ [ − a /2 , a /2 ] counts. Disk: centre ( − a /2 , 0 , 0 ) on the face, radius a/4 in the xy-plane → half inside: 3 C. Rod from a/4 to 5a/4 (uniform, 8 C): the inside part a/4 to a/2 is 4 1 ​ of it: 2 C. Point − 7 C at ( a /4 , − a /4 , 0 ) : inside. Point 3 C at ( − 3 a /4 , 3 a /4 , 0 ) : outside. Q e n c ​ = 3 + 2 − 7 = − 2 C ⇒ Φ = ε 0 ​ − 2 C ​ ⇒ x = -2.

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