lec 4 physics 72
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Lecture 4 Electric field lines; Electric field of a dipole August 13, 2015
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Physics 72
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Lecture 4Electric field lines; Electric field of a dipole
August 13, 2015
Response to an electric field
Example
If an electron (q = −e = −1.6× 10−19C, m = 9.1× 10−31 kg) is releasedfrom rest in a region where the electric field uniformly points upward withmagnitude 1.0× 104N/C. What is its acceleration in this region?
Lecture 4 August 13, 2015 2 / 17
Response to an electric field
Example
If an electron (q = −e = −1.6× 10−19C, m = 9.1× 10−31 kg) is releasedfrom rest in a region where the electric field uniformly points upward withmagnitude 1.0× 104N/C. What is its acceleration in this region?
Solution:Solve for the response of the electron to the electric field.
~F = q0 ~E = (−1.6× 10−19)(+1.0× 104 ̂) = −1.6× 10−15N ̂
Solve for the acceleration using Newton’s 2nd law.
~F = m~a −→ ~a =~F
m=−1.6× 10−15
9.1× 10−31= −1.8× 1015m/s2 ̂ .
Lecture 4 August 13, 2015 3 / 17
Response to an electric field
Lecture 4 August 13, 2015 4 / 17
Response to an electric field
Lecture 4 August 13, 2015 5 / 17
Electric field lines
Definition (Electric field lines)
A line or curve drawn through a region of space so that its tangent at anypoint is in the direction of the electric-field vector at that point
Lecture 4 August 13, 2015 6 / 17
Electric field lines
Definition (Electric field lines)
A line or curve drawn through a region of space so that its tangent at anypoint is in the direction of the electric-field vector at that point.
Lecture 4 August 13, 2015 7 / 17
Electric field lines
Lecture 4 August 13, 2015 8 / 17
Electric field lines
Remark
The spacing of electric field lines in a region gives us an idea of themagnitude of the electric field in that region.
Lecture 4 August 13, 2015 9 / 17
Electric field lines
Lecture 4 August 13, 2015 10 / 17
Electric field lines
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Electric field lines
Remark
Electric field lines should not intersect.
Lecture 4 August 13, 2015 12 / 17
Electric dipole
Definition (dipole)
A pair of electric charges of equal magnitude q but opposite sign,separated by a distance d .
Lecture 4 August 13, 2015 13 / 17
Response of a dipole to an electric field
There is zero net force, but there is a non-zero net torque. Set the centerof mass of the system as the axis rotation.
τ = (d/2)(qE ) sinφ+ (d/2)(qE ) sinφ = (qd)E sinφ
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Response of a dipole to an electric field
τ = (qd)E sinφ
Define electric dipole moment, with magnitude given by
p = qd
and direction pointing from the negative to the positive charge.Lecture 4 August 13, 2015 15 / 17
Response of a dipole to an electric field
τ = pE sinφ
~τ = ~p × ~E
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Quiz!
Reflect on what we have discussed so far.
Lecture 4 August 13, 2015 17 / 17
