PLEASE HELP! And show work/explain :( A point object with a positive charge +0is

Question

PLEASE HELP! And show work/explain :(

A point object with a positive charge +0is placed on the x-axis at x d. A second point object of unknown charge is placed at an unknown location on either the x-axis or the y-axis. The potential energy associated with the charges is U The potential at the origin due to the charges is V The net electric field at the origin due to the two charges points in the negativex direction. Assume the electric potential is zero at infinity. 4 points) (a) Before solving for the unknown charge and location answer these questions. (i) What is the sign of the unknown charge? positive l negative can not be determined How do you know? (ii) Where is the unknown charge located? positive x-axis negative x-axis positive y-axis negative y-axis How do you know? [4 points] (b) Determine the value (sign and magnitude) of the unknown charge and state its location. 12 points] (c) What is the magnitude of the electric field at the origin?

Explanation / Answer

potential energy of 2 point charge system is given as

PE= kq1q2 / d

one is positively charged then other is also positively charged as PE is positive.

suppose other charge is Qn1 and distance is dn2 from origin.

V = [ kQ/d ] + [ k(Qn1) / (dn2)] = 4 kQ/d

1 + (n1 / n2) = 4

n1 = 3n2

if unknown charge is on x axis then ,

U = k (Q)(Qn1) / (d + dn2) = 2 kQ^2/d

n1 / (1 + n2) = 2

3n2 = 2 + 2n2

n2 = 2

so n1 = 3*2 = 6

so its true.

i) sign : +ve

because potential energy is +ve.

ii) its is on +ve x axis.

as solved above.

b) unknown charge = Qn1 = 6Q

location = dn2 = 2d

c) E = [ k (Q) / d^2 ] - [ k(6Q) / (2d)^2 ]

= kQ/d^2 - 1.5kQ/d^2 = - 0.5 k Q / d^2

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