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For each of the following arrangements of two point charges, find all the points along the line passing through both charges for which the electric potential V is zero (take V = 0 infinitely far from the charges) and for which the electric field E is zero.

Part A
Charges +Q and +2Q separated by a distance d.

A) V=0 at infinity
B) V=0 at infinity and at the midpoint between the charges
C) V=0 nowhere

Part B
Charges +Q and +2Q separated by a distance d.

A) E=0 at the infinity
B) E=0 at the midpoint between charges
C) E=0 at the point which is between charges at the distance d/(1+2√) from +Q charge

Part C
Charges −Q and +2Q separated by a distance d.

A) V=0 at infinity

B) V=0 at infinity, at the point between charges at the distance d/3 from −Q charge, and at the point which is at the distance d from −Q and 2d from 2Q

C) V=0 at infinity, at the point between charges at the distance 2d/3 from −Q charge, and at the point which is at the distance d from 2Q and 2d from −Q

Part D
Charges −Q and +2Q separated by a distance d.

A) E=0 at the infinity

B) E=0 at the point between charges and at the distance d/3 from −Q charge

C) E=0 at the point which is at the distance d/(2√−1) from −Q and d+d/(2√−1) from 2Q charge

Part E
Are both V and E zero at the same places?

A) Yes
B) No