Two charges Q1( +2.00 µC) and Q2( +2.00 µC) are fixed symmetrically along the x-axis at...

Two charges Q₁( +2.00 µC) and Q₂( +2.00 µC) are fixed symmetrically along the x-axis at x = ± 3.00 cm.

How much work must be done to assemble these charges if they are initially infinitely far apart?
For this configuration, calculate the electrical potential difference between the origin and the point P, which is located on the y-axis 4.00 cm above the origin.
Now a third charge Q₃( -2.00 µC) is fixed at point P. What is the electrostatic potential energy of this new configuration?
If Q₃ is released from rest, what is its speed when it reaches the origin if its mass is 0.100 g?

Solutions

Expert Solution

a] Work done to introduce the 1st charge is 0 J since no forces are present.

Work done to introduce the 2nd charge = Work done to assemble both the charges = Potential Energy of the system

b] Electric Potential at P =

Electric Potential at O =

so, Potential difference between O and P is: .

c] Electrostatic Potential Energy of the new configuration is:

where p = [3² + 4²] = 5 cm = 0.05 m

Change in Potential energy = change in kinetic energy

since the charge was released from rest,

=> v = 183.30 m/s

this is the speed of Q3 when it reaches the origin.

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Two charges Q1(+2.00µC) and Q2(+2.00µC) are placed symmetrically along the x-axis at x = ±3.00cm. Consider...

Two charges Q1(+2.00µC) and Q2(+2.00µC) are placed symmetrically along the x-axis at x = ±3.00cm. Consider a charge Q3 of charge +5.00µC and mass 10.0 g moving along the y-axis. If Q3 starts from rest at y=2.00cm, what is its speed when it reaches y=4.00cm?

two electrical charges, q1= -20.0 nC and q2= +10.0 nC, are located on the x-axis at...

two electrical charges, q1= -20.0 nC and q2= +10.0 nC, are located on the x-axis at x= 0 m and x= 1.00 m, respectively. What is the magnitude of the electric field at the point x= 0.50 m, y= 0.50 m?

Three point charges are on the x-axis: q1 at the origin, q2 at 3 m, and...

Three point charges are on the x-axis: q1 at the origin, q2 at 3 m, and q3 at 7 m. A) Find the potential at the point (0, 4 m) if q1 = q2 = q3 = 2 µC. The Coulomb constant is 8.99 × 109 N · m2 /C 2 Answer in units of kV. B) Find the potential at the point (0, 4 m) if q1 = q2 = 2 µC and q3 = −2 µC . Answer...

Point charges q1 = 43 µC and q2 = −21 µC are placed 3.5 m apart....

Point charges q1 = 43 µC and q2 = −21 µC are placed 3.5 m apart. Where must q3 = 24 µC be placed (on the x-axis, in m) so that the net force on it is zero? (Assume that q1 is at x = 0 and q2 is at x = 3.5 m.)

Two charges are placed on the x axis. One of the charges (q1 = +8.59C) is...

Two charges are placed on the x axis. One of the charges (q1 = +8.59C) is at x1 = +3.00 cm and the other (q2 = -24.4C) is at x2 = +9.00 cm. Find the net electric field (magnitude and direction given as a plus or minus sign) at (a) x = 0 cm and (b) x = +6.00 cm. please help

Two charges are placed on the x axis. One of the charges (q1 = +7.73C) is...

Two charges are placed on the x axis. One of the charges (q1 = +7.73C) is at x1 = +3.00 cm and the other (q2 = -23.7C) is at x2 = +9.00 cm. Find the net electric field (magnitude and direction given as a plus or minus sign) at (a) x = 0 cm and (b) x = +6.00 cm.

Two charges are placed along the x axis such that charge A is at -3 m,...

Two charges are placed along the x axis such that charge A is at -3 m, and has a charge of 2.5e-06 C. Charge B is at 2.2 m, and has a charge of -2.5e-06 C. What is the x component of the force (in Newtons) felt by charge A due to charge B? What is the x component of the force (in Newtons) felt by charge B due to charge A? Suppose a third charge were to be placed...

3. Two charges with fixed positions are listed below: q1 = −4 µC at (−2 mm,...

3. Two charges with fixed positions are listed below: q1 = −4 µC at (−2 mm, 2 mm); q2 = −14 µC at (3 mm, 2 mm). (a) (5 points) Determine the electric potential at the origin. (b) (10 points) If an α-particle were placed at the origin, determine the electric force on the α-particle due to the fixed charges. Note: an α-particle is a helium nucleus, which is made of two protons and two neutrons. (c) (10 points) Where...

can explain how solve these #Electromagnetism qusitons ------Q1 Point charges Q1 = 100 µC and Q2...

can explain how solve these #Electromagnetism qusitons ------Q1 Point charges Q1 = 100 µC and Q2 = 0.12 µC are placed at (0.03, 0.08, −0.02) and (−0.03, 0.01, 0.04), respectively. Determine the force on Q1 ------Q2 Convert ? = 10?−??? − 3??? from cylindrical to Cartesian and evaluate it at (3, 4, 5). ------Q3 Determine the gradient of ? = cos? + sin? + sin2 ? and evaluate the gradient at (2, π/2, π). ------Q4 For the vector field ?...

Two charges, q1 = 32 μC and q2 = 38 μC, are located along a straight...

Two charges, q1 = 32 μC and q2 = 38 μC, are located along a straight line at x = 22 cm and 38 cm respectively. Where along the x-axis should a third charge q3 with a charge of 1 μC be located such that the net force on this charge is zero. Two charges, q1 = 10.5 μC and q2 = -4.5 μC , are located at coordinates (x,y) = (21.6, 8.6) cm and (23.0, 10.6) cm respectively. Find...

Subjects