Two charges, q 1 and q 2, are located at the origin and at (0.70 m , 0), respect

Question

Two charges, q1 and q2, are located at the origin and at (0.70 m , 0), respectively.

A. Where on the x-axis must a third charge, q3, of arbitrary sign be placed to be in electrostatic equilibrium if q1 and q2 are like charges of equal magnitude?

B. Where on the x-axis must a third charge, q3, of arbitrary sign be placed to be in electrostatic equilibrium if q1 and q2 are unlike charges of equal magnitude?

C. Where on the x-axis must a third charge, q3, of arbitrary sign be placed to be in electrostatic equilibrium if q1 = +3.9 C and q2 = -7.7 C ?

Explanation / Answer

1)
If q1 and q2 are like chrges of equal magnitude, then charge q3 should be placed in right in between of these two charges to be in electrostatic equilibrium.

q3 should be placed @ x =0.35m

2)
Let the charge on q1 = q
Let the charge on q2 = -q
A charge will be in electrostatic equilibriu,m where Electric field = 0
Let charge be placed x cm from q1.
Distance of charge from q2 = 0.7m - x

E = k ( q / x^2 - q / (0.7 - x)^2)
q/x^2 = q / (0.7 - x)^2
(0.7 - x)^2 = x^2

There is no such point possible on x axis where third charge will be in electrostatic equlibrium.

3)
q1 = 3.9 C @ x =0
q2 = -7.7 C @ x =0.7 m
A charge will experience zero force at a point , where Electric field = 0

E = k Q/r^2
Let charge be placed x cm from q1.
Distance of charge from q2 = 0.7 cm - x

E = k ( 3.9 C / x^2 - 7.7uC / (0.7 - x)^2)
3.9 C / x^2 = 7.7uC/(0.7 - x)^2)
3.9 * (0.7 - x)^2 = 7.7 x^2
Solving for x
x = -1.72 m
Charge should be placed at x = -1.72 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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