Question

In: Physics

A charge 4.98 nC is placed at the origin of an xy-coordinate system, and a charge...

A charge 4.98 nC is placed at the origin of an xy-coordinate system, and a charge -1.99 nC is placed on the positive x-axis at x = 4.01 cm . A third particle, of charge 6.05 nC is now placed at the point x = 4.01 cm , y = 2.98 cm .

a. Find the x-component of the total force exerted on the third charge by the other two.

b. Find the y-component of the total force exerted on the third charge by the other two.

c. Find the magnitude of the total force acting on the third charge.

d. Find the direction of the total force acting on the third charge. (THETA)

Solutions

Expert Solution

The Coulomb's law is an equation that relates the magnitude of the force between two point charges, q1 and q2, seperated by a distance d as follows;

F = k *q1* q2/d2

In our case, let charge 1 be charge q1 = 4.98nC, charge 2 be q2 = − 1.99nC and charge 3 be q3 = 6.05 nC.

The distance between charges 1 and 3 is

r = √(4.01 cm)2 + (2.98 cm)2 =4.996 cm=0.04996 m

Therefore, the magnitude of the electric force exerted by charge 1 on charge 3 is

F13 = (8.9875 × 109 N⋅m2/C2) × |4.98 × 10−9C| × |6.05 × 10−9 C|(0.04996 m)2

= 1.0848124150 × 10−4 N

and this force makes an angle

α = arctan (2.98/4.01) = 36.62604402∘

with the positive x-axis since this force is repulsive (between two positive charges). Therefore, the x-component of the electric force exerted by charge 1 on charge 3 is

F13,x = F13 cosα = 1.084124150 × 10−4 N × cos36.6204402∘

=8.708510047 × 10−5 N

in the positive x-direction, and the y-component is

F13,y = F13 sinα

= 1.084124150 × 10−4 N × sin36.6204402

= 6.460680187 × 10−5 N∘

in the positive y-direction.

Similarly, the magnitude of the electric force exerted by charge 2 on charge 3 is

F23 = (8.9875 × 109 N⋅m2/C2) × |− 1.99 × 10−9 C| × |6.05 × 10−9 C|/(0.0298 m )2= 1.21825289 × 10−4 N

in the negative y-direction since this force is attractive.( no x component)

a: The x-component of the total force exerted on charge 3 by the other two charges is

Fx = F13,x + F23,x= (8.708510047 × 10−5 +0 ) N =8.708510047 × 10−5 N

b: The y-component of the total force exerted on charge 3 by the other two charges is

Fy = F13,y − F23,y= 6.460680187 × 10−5 N∘ − 1.21825289 × 10−4 N = − 5.245572705 × 10−5 N

c: The magnitude of the total force on charge 3 is

F = √F2x + F2y= √(8.708510047 × 10−5 N)2+(− 5.245572705 × 10−5N)2 =1.015565066 × 10−4 N

d.

force makes an angle

θ = − arctan(5.245572705× 10−5N)/(8.708510047 × 10−5 N) = − 31.0635842

with the positive x-axis, measured counterclockwise.


Related Solutions

A charge 4.98 nC is placed at the origin of an xy-coordinate system, and a charge...
A charge 4.98 nC is placed at the origin of an xy-coordinate system, and a charge -2.05 nC is placed on the positive x-axis at x = 3.97 cm . A third particle, of charge 6.04 nC is now placed at the point x = 3.97 cm , y = 3.01 cm
A charge of -2.95 nC is placed at the origin of an xy-coordinate system, and a...
A charge of -2.95 nC is placed at the origin of an xy-coordinate system, and a charge of 2.20 nC is placed on the y axis at y = 3.85 cm . Part A If a third charge, of 5.00 nC , is now placed at the point x = 3.40 cm , y = 3.85 cm find the x and ycomponents of the total force exerted on this charge by the other two charges. Express answers numerically separated by...
A charge of -2.90 nC is placed at the origin of an xy-coordinate system, and a...
A charge of -2.90 nC is placed at the origin of an xy-coordinate system, and a charge of 1.80 nC is placed on the y axis at y = 3.75 cm . A) If a third charge, of 5.00 nC , is now placed at the point x = 3.50 cm , y = 3.75 cmcm find the xx and y components of the total force exerted on this charge by the other two charges. Fx, Fy= ______ N B)...
A charge of -4.00 nC is placed at the origin of an xy coordinate system, and...
A charge of -4.00 nC is placed at the origin of an xy coordinate system, and a charge of 3.00 nC is placed on the y-axis at y=4.00 cm. A third charge of 5.00 nC is now placed at the point x=-3.00, y=0.00 cm. Find the x and y components of the total force exerted on the third charge by the other two charges. Find the magnitude and direction of the force.
A charge of -3.00 nC is placed at the origin of an xy-coordinate system, and a...
A charge of -3.00 nC is placed at the origin of an xy-coordinate system, and a charge of 2.25 nC is placed on the y axis at y = 3.60 cm . PART A - If a third charge, of 5.00 nC , is now placed at the point x = 3.50 cm , y = 3.60 cm find the x and y components of the total force exerted on this charge by the other two charges. PART B- Find...
A charge of -3.45 nC is placed at the origin of an xy-coordinate system, and a...
A charge of -3.45 nC is placed at the origin of an xy-coordinate system, and a charge of 2.30 nC is placed on the y axis at y= 3.90 cm. Part A: If a third charge, of 5.00 nC , is now placed at the point x = 2.75 cm , y = 3.90 cm find the x and y components of the total force exerted on this charge by the other two charges. Part B: Find the magnitude of...
A charge q1 = 5.00 nC is placed at the origin of an xy-coordinate system, and...
A charge q1 = 5.00 nC is placed at the origin of an xy-coordinate system, and a charge q2 = -4.00 nC is placed on the positive x axis at =x= 4.00 cm. (a) If a third charge q3 = 5.50 nC is now placed at the point x= 4.00 cm , y= 3.00 cm find the x and y components of the total force exerted on this charge by the other two charges. (b) Find the magnitude of this...
A charge q1 = 5.00 nC is placed at the origin of an xy-coordinate system, and...
A charge q1 = 5.00 nC is placed at the origin of an xy-coordinate system, and a charge q2 = -4.50 nC is placed on the positive x axis at x= 4.00 cm . If a third charge q3 = 8.00 nC is now placed at the point x= 4.00 cm , y= 3.00 cmcm find the x and y components of the total force exerted on this charge by the other two charges. Find Fx, Fy, and find the...
A charge q1 = + 10.00 nC is placed at the origin of an xy coordinate...
A charge q1 = + 10.00 nC is placed at the origin of an xy coordinate system, and a charge q2 = - 10.00 nC is placed on the positive x-axis at x = 8.00 cm. If a third charge q3 = +10.00 nC is now placed at the point x = 8.00 cm, y = 6.00 cm, find the magnitude of the total force exerted on this charge by the other two
A charge of -3.30nC is placed at the origin of an xy-coordinate system, and a charge...
A charge of -3.30nC is placed at the origin of an xy-coordinate system, and a charge of 2.5nC is placed on the axis at y=3.55cm. a) If a third charge, of 5 nC, is now placed at the point x=3.05cm, y=3.55cm find the x and y conponents of the total force exerted on this charge by the other two charges. b) Find the magnitude of this force c) Find the direction of this forces.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT