In the figure shown, all four charges (+Q, +Q, -q, and -q) are situated at the c
ID: 1453244 • Letter: I
Question
In the figure shown, all four charges (+Q, +Q, -q, and -q) are situated at the corners of a square charge +Q is zero. (a) Express the magnitude of q in terms of Q. (b) Is the net electric force on each charge -q also equal to zero? Justify your answer. (c) Determine the electric field at the center of the square. Two charges, +Q and +2Q, are fixed in place along the y axis of an x-y coordinate system as shown in the figure below. Chaise is at the point (0, a), and Charge 2 is at the point (0, -2a). (a) Find the electric force (magnitude and direction) felt by Charge 1 due to Charge 2. (b) Find the electric field (magnitude and direction) at the origin created by both Charges 1 and 2. (c) Is there a point on the x axis where the total electric field is zero? If so, where? If not, explain briefly. (d) Is there a point on the y axis where the total electric field is zero? If so, where? If not, explain briefly. (e) If a small negative charge, -q, of mass m were placed at the origin, determine its initial acceleration (magnitude and direction).Explanation / Answer
1)
let L is the length of each side of square.
a) from figure
sqrt(2)*k*Q*q/L^2 = k*Q^2/(2*L^2)
sqrt(2)*q = Q/2
==> Q = 2*sqrt(2)*q
= 2.828*q
b) No. The repulsive force between q and q is not equal to the attrcative force between Q and q.
c) zero.
2)
a) F12 = k*Q1*Q2/d^2
= k*Q*(2*Q)/(3*a)^2
= (2/9)*k*Q/a^2
b) Enet = k*Q/a^2 - k*2*Q/(2*a)^2
= (1/2)*k*Q^2/a^2
c) no. at every point the filed due to +Q ia greater than +2*Q
d) yes. at -y axis.
let a is the distance from origin.
k*Q/(y)^2 = k*2*Q/((2*a-y)^2
1/y^2 = 2/(2*a - y)^2
4*a^2 + y^2 - 4*a*y = 2*y^2
4*a^2 - y^2 - 4*a*y = 0
solve the above equation to get y.
e) F = q*Enet
m*a = q*Enet
a = q*Enet/m
= q*(1/2)*k*Q^2/a^2/m
= k*Q^2*q/(2*m*a^2)
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