Electric Potential Energy & Electric Potential Problem Sheet & Solutions PDF

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Electric Potential Energy & Electric Potential Problem Sheet & Solutions set by Dr Jean Paul Mosnier...

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PS104 Problems and Exercises data bank Chapter 2 Electric Potential Energy, Electric Potential ELECTRIC POTENTIAL ENERGY 23.5 A point charge  Q = +4.60 µC is held fixed at the origin. A second point charge  q = +1.20 µC with mass of  2.80 ×10 −4 kg is placed on the x-axis, 0.250 m from the origin. (a) What is the electric potential U of the pair of charges? (take U to be zero when the charges have infinite separation). (b) The second point charge is released from rest. What is the speed when its distance from the origin is (i) 0.500 m, (ii) 5.0 m, (ii) 50.0 m?

23.5: a)

23.7 A point charge  q1 = +4.00 nC is placed at the origin and a second point charge  q2 = −3.00 nC is placed on the x-axis at x = +20.0 cm. A third point charge  q3 = 2.00 nC is to be placed on the x-axis between  q1 = +4.00 nC and  q2 = −3.00 nC (take the zero of potential energy of the three charges when they are infinitely apart).(a) What is the potential energy of the system of three charges if  q3 is at x = +10.0 cm ? (b) Where should  q3 = 2.00 nC be placed to make the potential energy of the system equal to zero?

23.7: a)

So solving for x we find: Therefore since it is the only value between the two charges. Electric Potential

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ELECTRIC POTENTIAL 23.18 Two stationary point charges  +3.00 nC and  +2.00 nC are separated by a distance of 0.50 m. An electron is released from rest at a point midway between the two charges ad moves along the line connecting the two charges. What is the speed of the electron when it is 0.1 m from the  +3.00 nC charge?

23.18: Initial energy equals final energy:

23.20 The potential V at a distance of 25.0 cm from a very small charged sphere is 48.0 V, with V to be taken as zero at an infinite distance away from the sphere. (a) If the sphere is treated as a point charge, what is its charge? (b) What is the potential at a distance of 75 cm from the sphere?

23.20: a) b)

23.23 A positive charge  +q is located at the point  x = 0, y = −a and a negative charge  −qis located at the point  x = 0, y = +a . (a) Show the positions of the charges in a diagram. (b) Derive an expression for the potential V at points on the  x − axis as a function of the coordinate  x. Take V to be zero at an infinite distance from the charges. (c) Graph V at points on the  x − axis as a function of  x over the range from  x = −4a to  x = +4a . (d) What is the answer to part (b) if the two charges are interchanged so that  +q is at  y = +a and  −q is at  y = −a ?

Electric Potential

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23.23: a)

b) c) The potential along the x-axis is always zero, so a graph would be flat. d) If the two charges are interchanged, then the results of (b) and (c) still hold. The potential is zero

23.28 At a certain distance from a point charge, the potential and electric field magnitude due to that charge are 4.98 V and 12.0 V/m, respectively. (Take the potential to be zero at infinity). (a) What is the distance to the point charge? (b) What is the magnitude of the charge? (c) Is the electric field directed toward or away from the point charge?

23.28:

a)

b) c) The electric field is directed away from q since it is a positive charge.

CALCULATING ELECTRIC POTENTIAL 23.34 An infinitely long line of charge has linear charge density 5.0x10-12 C/m. A proton ( m p = 1.67 ×10 −27 kg, q p = +1.60 ×10 −19 C ) is 18.0 cm from the line and moving directly toward the line at 1500 m/s. How close does the proton get to the line of charge?

23.34: Energy is conserved:

But:

Electric Potential

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23.36 Two large, parallel, metal sheets carrying opposite electric charges of equal magnitude are separated by a distance of 38.0 mm. The electric field in between them is uniform and has magnitude 480 N/C. (a) What is the potential difference between the sheets? (b) Which sheet is a higher potential? (c) What is the surface charge density 𝜎 on the positive sheet?

23.36: a) b) The higher potential is at the positive sheet. c)

23.38 Two large, parallel conductive plates carrying opposite charges of equal magnitude are separated by 2.20 cm. (a) If the surface charge density for each plate has magnitude 47 nC/m2, what is the magnitude of the electric field in between the plates. (b) What is the potential difference between the two plates? (c) If the separation distance between the two plates is doubled while the surface charge density is kept constant at the value of part (a), what happens to the magnitude of the electric field and to the potential difference?

23.38: a) b) c) The electric field stays the same if the separation of the plates doubles, while the potential between the plates doubles.

Electric Potential

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