Concept explainers
(a)
The expression for the electric potential.
(a)
Answer to Problem 82P
The expression for the electric potential is
Explanation of Solution
The diagram for the system is given by figure 1.
Write the expression total potential.
Here,
Write the equation for potential difference at first point.
Here,
Write the equation for potential difference at second point.
Here,
For
Here.
The distance between the points are almost same,
Write the expression for dipole.
Conclusion:
Substitute,
Thus, the expression for the electric potential is
(b)
The radial and perpendicular component of electric field.
(b)
Answer to Problem 82P
The radial and perpendicular component of electric field is
Explanation of Solution
Write the expression for the radial component of electric field.
Here,
Write the equation for perpendicular component of electric field.
Here,
Conclusion:
Substitute,
Substitute,
Thus, the radial and perpendicular component of electric field is
(c)
The electric field at
(c)
Answer to Problem 82P
The electric field at
Explanation of Solution
Write the expression for the radial component of electric field.
Write the expression for the perpendicular component of electric field.
Conclusion:
For
Substitute,
For
Substitute,
The results are reasonable since the component of electric field is having finite value.
Thus, the electric field at
(d)
The electric field at
(d)
Answer to Problem 82P
The electric field at
Explanation of Solution
Write the expression for the radial component of electric field.
Write the expression for the perpendicular component of electric field.
Conclusion:
Substitute,
The electric field at the centre of dipole is not infinite.
The results are not reasonable since the component of electric field is having infinite value.
Thus, The electric field at
(e)
The potential in Cartesian coordinate.
(e)
Answer to Problem 82P
The potential in Cartesian coordinate is
Explanation of Solution
Write the expression for the potential.
Conclusion:
Substitute,
Thus, the potential in Cartesian coordinate is
(f)
The x and y component of electric field.
(f)
Answer to Problem 82P
The x and y component of electric field is
Explanation of Solution
Write the expression for the x component of electric field.
Here,
Write the equation for y component of electric field.
Here,
Conclusion:
Substitute,
Substitute,
Thus, the x and y component of electric field is
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Chapter 20 Solutions
Principles of Physics
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- An electric dipole is located along the y axis as shown in Figure P24.48. The magnitude of its electric dipole moment is defined as p = 2aq. (a) At a point P, which is far from the dipole (r a), show that the electric potential is V=kepcosr2 (b) Calculate the radial component Er and the perpendicular component E of the associated electric field. Note that E = (1/r)(V/). Do these results seem reasonable for (c) = 90 and 0? (d) For r = 0? (e) For the dipole arrangement shown in Figure P24.48, express V in terms of Cartesian coordinates using r = (x2 + y2)1/2 and cos=y(x2+y2)1/2 (f) Using these results and again taking r a, calculate the field components Ex and Ey. Figure P24.48arrow_forwardFour particles are positioned on the rim of a circle. The charges on the particles are +0.500 C, +1.50 C, 1.00 C, and 0.500 C. If the electric potential at the center of the circle due to the +0.500 C charge alone is 4.50 104 V, what is the total electric potential at the center due to the four charges? (a) 18.0 104 V (b) 4.50 104 V (c) 0 (d) 4.50 104 V (e) 9.00 104 Varrow_forwardA proton is located at the origin, and a second proton is located on the x-axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) An alpha particle (charge = 2e, mass = 6.64 1027 kg) is now placed at (x, y) = (3.00, 3.00) fm. Calculate the electric potential energy associated with this configuration. (c) Starting with the three-particle system, find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in place. (Throughout, neglect any radiation effects.) (d) Use conservation of energy to calculate the speed of the alpha particle at infinity. (e) If the two protons are released from rest and the alpha panicle remains fixed, calculate the speed of the protons at infinity.arrow_forward
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