Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed...

Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of an equilateral triangle, as the drawing shows. The magnitude of each of the charges is 3.5 μC, and the lengths of the sides of the triangle are 2.0 cm. Calculate the magnitude of the net force that each charge experiences.

Solutions

Expert Solution

The force experienced by the positive charge (say at the top corner of the equilateral triangle )due to another positive charge is
F = k q² / r²
Where q is the charge and r is the distance between the charges
F = 9 x 10⁹ x (3.5 x 10^-6)² / (0.02 m)²
F =  275.62 N
This is directed away from the positive charge along the line joining the two charges
The force on the positive charge due to the negative charge is
F =  k q² / r²
F =  9 x 10⁹ x (3.5 x 10^-6)² / (0.02 m)²
F =  275.62 N
This force directed towards the negative charge
To find the net force on the positive charge
When we make the forces in their component form, we can see that the vertical components (F sin ) cancels and the parallel components gets added
The net force is
F_net = 2 F cos
Where is the angle between the force and the horizontal direction.
F_net = 2 x  275.62 x cos 60⁰
F_net =   275.62 N
Directed horizontally towards the right or left (depending on where the negative charge resides)
The force experienced by the other positve charge due to positive and negative charges is the same as the above case.
For the negative charge, the force is due to both positive charges
The force experienced is
F = F =  k q² / r²
F =  9 x 10⁹ x (3.5 x 10^-6)² / (0.02 m)²
F =  275.62 N
Both the forces are directed towards the positve charge.
The two forces are separated by an angle of 60⁰. Thus the net force is
F_net = sqrt (F² + F² + 2 F² cos 60⁰)
F_net = sqrt(3) F
F_net = 1.732 x 275.62 N = 477.39 N
F_net = 477.39 N

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Each part of (Figure 1) shows one or more point charges. The charges have equal magnitudes.

Each part of (Figure 1) shows one or more point charges. The charges have equal magnitudes. A) For case (a), if a positive charge is moved from position i to position f, does the electric potential energy increase, decrease, or stay the same? For case (a), if a positive charge is moved from position to position, does the electric potential energy increase, decrease, or stay the same? Electric potential energy increases. Electric potential energy decreases. Electric potential...

Two point charges are fixed in place. The positive charge is +2q and the negative charge...

Two point charges are fixed in place. The positive charge is +2q and the negative charge is –q. On the line that passes through the charges, how many places are there at which the total potential is zero?

Two point charges are fixed on the y axis: a negative point charge q1 = -30...

Two point charges are fixed on the y axis: a negative point charge q1 = -30 μC at y1 = +0.22 m and a positive point charge q2 at y2 = +0.37 m. A third point charge q = +9.8 μC is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 20 N and points in the +y direction. Determine the magnitude of q2.

Two positive point charges are held fixed on the x-axis. Point charge A is located at...

Two positive point charges are held fixed on the x-axis. Point charge A is located at the origin, and point charge B is located at the position x = −5.00 cm = −5.00✕10-2 m (on the negative x-axis). The magnitude of charge A is two times greater than that of charge B: qA = 2qB. ke = 8.9876✕109 Nm2/C2 (A.) The electric force on charge A has magnitude 0.344 mN = 0.344⨯10-3 N. What is the electric force (magnitude and...

Two point charges are held fixed on the y-axis: negative charge #1, q1 = −6.30 ✕...

Two point charges are held fixed on the y-axis: negative charge #1, q1 = −6.30 ✕ 10−9 C, is located at the origin; charge #2, a positive charge, q2 = +8.30 ✕ 10−9 C, is located at the point (x=0, y=+4.00✕10−2 m). Consider the point (x=0, y=−7.00✕10-2 m) on the negative y-axis for parts (a.), (b.), and (c.). Additionally, consider the point (x=+4.00✕10-2 m, y=0) on the positive x-axis for parts (d.) and (e.). Recall, Coulomb's constant: ke = 8.9876...

A positive point charge Q1=2.8×10−5C is fixed at the origin of coordinates, and a negative point...

A positive point charge Q1=2.8×10−5C is fixed at the origin of coordinates, and a negative point charge Q2=−4.1×10−6C is fixed to the x axis at x=+2.0m. Find the location of the place(s) along the xx axis where the electric field due to these two charges is zero.

Why will the resulting force lines of two positive point charges be like this:

One positive and one negative charges identical in magnitude are place near each other. At halfway...

One positive and one negative charges identical in magnitude are place near each other. At halfway between the two charges... the electric field is zero and the potential is zero. the electric filed is not zero and the potential is positive. the electric field is not zero and the potential is zero. None of these statements is true. the electric field is not zero and the potential is negative.

Two positive point charges q1 = 6.0nC and q2 = 9.0nC are separated in a vacuum...

Two positive point charges q1 = 6.0nC and q2 = 9.0nC are separated in a vacuum by a distance of 5.36m. The spot on the line between the charges measured from the charge q1 where the net electric field is zero is

Two point charges of equal magnitude are 8.1 cm apart. At the midpoint of the line...

Two point charges of equal magnitude are 8.1 cm apart. At the midpoint of the line connecting them, their combined electric field has a magnitude of 40 N/C .Find the magnitude of the charges.

Subjects