Consider a charge of -1 nC at (-1,0) m, and a charge of +1 nC at...

Consider a charge of -1 nC at (-1,0) m, and a charge of +1 nC at (1,0). Calculate the electric potential everywhere in the plane.

Expert Solution

Potential due to an electric dipole

We already know that electric dipole is an arrangement which consists of two equal and opposite charges +q and -q separated by a small distance 2a.
Electric dipole moment is represented by a vector p of magnitude 2qa and this vector points in direction from -q to +q.
To find electric potential due to a dipole consider charge -q is placed at point P and charge +q is placed at point Q as shown below in the figure.
Since electric potential obeys superposition principle so potential due to electric dipole as a whole would be sum of potential due to both the charges +q and -q. Thus

where r₁ and r₂ respectively are distance of charge +q and -q from point R.
Now draw line PC perpandicular to RO and line QD perpandicular to RO as shown in figure. From triangle POC
cos?=OC/OP = OC/a
therefore OC=acos? similarly OD=acos?
Now ,
r₁ = QR?RD = OR-OD = r-acos?
r₂ = PR?RC = OR+OC = r+acos?

since magnitude of dipole is
|p| = 2qa
If we consider the case where r>>a then

again since pcos?= p

genius_generous answered 8 months ago

1. Consider a charge of -1 nC at (-1,0) m, and a charge of +1 nC...

1. Consider a charge of -1 nC at (-1,0) m, and a charge of +1 nC at (1,0). Calculate the electric potential everywhere in the plane. 2. For the same geometry as in the first problem, calculate the electric field everywhere, using -?V =E. In 2 dimensions, ?V= (?subxV, ?subyV) = ?subxV x^ + ?suby Vy^

A 7.80-nC charge is located 1.70 m from a 4.30-nC point charge.

A 7.80-nC charge is located 1.70 m from a 4.30-nC point charge. (a) Find the magnitude of the electrostatic force that one charge exerts on the other.(b) Is the force attractive or repulsive?

A 7.80-nC charge is located 1.70 m from a 4.30-nC point charge. (a) Find the magnitude...

A 7.80-nC charge is located 1.70 m from a 4.30-nC point charge. (a) Find the magnitude of the electrostatic force that one charge exerts on the other. Answer in N (b) Is the force attractive or repulsive?

1. A charge of +3 nC is at the point (0,2,0), and a charge of -1...

1. A charge of +3 nC is at the point (0,2,0), and a charge of -1 nC is at the point (0,-2,0). a) Find the electric field (E) at the point (0,-1,1). b) Find the force of a 3 uC charge at (1,0,0).

A negative 18 nC charge is at the origin and a charge of 6 nC is...

A negative 18 nC charge is at the origin and a charge of 6 nC is located at 0.4 m and 1.2 m. A point P is situated at x and y . What is the magnitude of the resultant electric field intensity point P due to the two charges?

A 11.0 nC charge is at x = 0cm and a -1.3 nC charge is at...

A 11.0 nC charge is at x = 0cm and a -1.3 nC charge is at x = 5 cm . At what point or points on the x-axis is the electric potential zero?

Consider a charge configuration in which a point charge of strength +50 nC is placed at...

Consider a charge configuration in which a point charge of strength +50 nC is placed at (x, y, z) = (+2.0, 0, 0) m, and another point charge, of strength −25 nC, is placed at (x, y, z) = (−2.0, 0, 0) m. (i) Calculate an expression for the electric potential along the x-axis between the two charges. Hint: exercise care with how you define the value for r for each charge. (ii) Make a rough plot (by hand) of...

A line of charge 2.0 m long has 50.0 nC of charge uniformly distributed along it....

A line of charge 2.0 m long has 50.0 nC of charge uniformly distributed along it. (a) Calculate the electric field 0.25 m above the center of the line. (b) If the field point were moved from 0.25 m to 1.0 m, by what factor does the field increase/decrease? (c) How does this compare with moving the field point from 0.25 m to 1.0 m away from a point charge?

A point charge of - 4.00 nC is located at (0, 1.00) m. What is the...

A point charge of - 4.00 nC is located at (0, 1.00) m. What is the x component of the electric field due to the point charge at (4.00, - 2.00) m?

A -3.00 nC point charge is at the origin, and a second -6.50 nC point charge...

A -3.00 nC point charge is at the origin, and a second -6.50 nC point charge is on the x-axis at x = 0.800 mm. a. Find the electric field (magnitude and direction) at point on the x-axis at x = 0.200 m. b.Find the electric field (magnitude and direction) at point on the x-axis at x= 1.20 m. c.Find the electric field (magnitude and direction) at point on the x-axis at x = -0.200 m.

Question