A particle carrying charge + q is located at the center of a square with sides o

Question

A particle carrying charge +q is located at the center of a square with sides of length l . (Only need to answer part C)

a ) Given four particles, two carrying charge +q and two carrying charge  ?q, how should you place them at the four corners of the square, with one particle at each corner, such that the vector sum of the electric forces exerted on the center particle is zero (one particle carrying the charge +q is already placed in the corner of the square)?

b) If you leave the corner particles in the arrangement determined in part A, but move the center particle to the midpoint of the top side of the square, what is the magnitude of the vector sum of the forces exerted on this particle? (Express your answer in terms of Coulomb's constant k, q and l.)

c) If you leave the corner particles in the arrangement determined in part A but move the center particle to the midpoint of the top side of the square, what is the direction angle of the vector sum of the forces exerted on this particle measured counterclockwise from the positive x direction?

? = __________

---------------------------------------------------------ANSWERS-----------------------------------------------------------------------------

a)

b)

Force by two charges each at the top is given as

F' = k q2 / (l/2)2 = 4 k q2 / l2

Total force by top two charges = Ft = 2 F' = 8 k q2 / l2

AB = sqrt ((L/2)2 + L2) = 1.118 L

Force by each of the bottom charges

F = k q /AB2 = kq / (1.118 L)2 = (0.8) k q2 / l2

Net force by Bottom two charges

Net force = Fnet = Ft - Fb = 8 k q2 / l2 - (0.72) k q2 / l2 = 7.28k q2 / l2

c)

Explanation / Answer

As already given in the above answer b....

the net force from bottom charges is Fb towards left side..

Ft is towards the right side..

net force = Ft - Fb and is positive.. so it is in the direction of Ft i.e to the right side i.e towards negative charge q i.e (-q)

so the angle with positive x axis is 0

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.