Q-? (3 points) Two charges of +1.0 uC are fixed on two diagonally opposite corne

Question

Q-? (3 points) Two charges of +1.0 uC are fixed on two diagonally opposite corners of a square with sides of length L. On another corner of the square a charge of +5.0 uC is fixed. On the remaining corner of the square a charge Q is placed, such that there is no net electric force acting on the +5.0 ?C charge. What is the value of the charge 0? Report your answer in uC and with proper sign. Hint: +5.0 uc+1.0uC in order to solve the problem one doesn't really need to know the value of L: it eventually cancels out of the equations. However if it is 9. +1.0 HC easier for you to deal with numbers, assume any number for L

Explanation / Answer

Electrostatic force is given by:

F = kq1q2/R^2

Assuming L = 1 m

then distance between 5 uC and Q will be = sqrt (1^2 + 1^2) = 1.414

Now

Fnet = Fx i + Fy j

due to 1 uC (towards right), force on 5 uC will be

F1x = -kq1q2/r^2 = -9*10^9*1*5*10^-12

F1x = -4.5*10^-2 N (-ve sign means force will be in -ve x-axis)

F1y = 0

due to 1 uC (towards up), force on 5 uC will be

F2y = -kq1q2/r^2 = -9*10^9*1*5*10^-12

F2y = -4.5*10^-2 N (-ve sign means force will be in -ve y-axis)

F2x = 0

Since given that net force on 5 uC is zero, and since F1 and F2 are in -ve x and -ve y direction, So to balance those forces Q should be -ve

due to Q,

F3x = F3*cos 45 deg = kq1q2*cos 45 deg/R^2

cos 45 deg = 1/sqrt 2

F3x = 9*10^9*5*10^-6*Q/(sqrt 2*1.414^2)

F3x = 15914.71*Q

Similarly

F3y = F3*sin 45 deg = kq1q2*sin 45 deg/R^2

sin 45 deg = 1/sqrt 2

F3y = 9*10^9*5*10^-6*Q/((sqrt 2)*1.414^2)

F3y = 15914.71*Q

Net force will be

Fnet = 0 = Fx i + Fy j

0 = (-4.5*10^-2 + 15914.71*Q) i + (-4.5*10^-2 + 15914.71*Q) j

Now both the coefficient of i and j should be zero, for Net force to become zero

15914.71*Q - 4.5*10^-2 = 0

|Q| = 4.5*10^-2/(15914.71)

Q = -2.828*10^-6 C

Q = -2.828 uC

Please Upvote. Let me know if you have any doubt.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

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