Chapter 21 – Electric Fields – Discrete Distributions

• Electric charge• Coulomb Force Law• Electric field of discrete charges• Field along axis• Off-axis electric fields – field lines• Motions of charges in fields• Dipoles

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Why? Chapter 21 – Electric Fields – Discrete Distributions

• Electric charge• Coulomb Force Law• Electric field of discrete charges• Field along axis• Off-axis electric fields – field lines• Motions of charges in fields• Dipoles

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Electric chargeOpposites attract …Like charges repel ..

Composition of matterMostly neutral (can have ions)Conducts or “insulates”

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Pop can physics?

Q: What happens if I bring the charged rod closer to the neutral metal pop can on the table?

a) Pop can attracted to charged rod.b) Pop can repelled by rod.c) Pop can not affected by rod at all.

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Lightning rods

Do they actually attract lightning?

Yes, but they also provide a safe path to the ground!

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Coulomb’s Law

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Trying to find “zero force” location for Q0

Q: Is there a location of “zero force” for charge q0 that exists somewhere to the right of charge q2?

A) Yes, a location can be found.B) No, not possible with these charges.C) It depends on the sign of the charge of q0.

Hint: “outside” the system, look close – look far ..

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Steps to find zero force (or E-field):1) Pick an origin!2) One distance is chosen as X3) Other distance will be combination of X and distance

between (Make it a POSITIVE distance construction)blank next 8

We’ll see these problems again when we get to Electric Fields!

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Electric FORCES are VECTORS!!!

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Electric field defined

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Collection of point charges – vector addition!

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Q: If a zero electric field value on the axis is possible, it will be:A) Zero electric field point in this situation is not possible.B) Between q1 and q2

C) To the right of q2

D) To the left of q1

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Graphical method for finding E field along axis (Ex !)

Ex pointing right – positive valuesEx pointing left – negative values

“progenitor” graph for positive charge

“progenitor” graph for negative charge

Multiple charges on axis?

Add graphs!

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Finding “zeros” of Ex graphs – closer to weaker charge!

In fact, all “artifacts” (zeros, peaks, minimums) will be closer to the “weaker” charge in the system (relative magnitude).

Investigate the system by looking CLOSE to each charge and FAR from the system (on both sides):• Close to a charge – that charge dominates• Far from a charge – “net charge” of system dominates• If there is a “change” from close to far – crossing point = zero!

Efield Physlet

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Off axis Electric Field … VECTORS!!What happens if you increase the magnitude of q2? Decrease the magnitude? Reverse the sign?

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Electric Field Lines

If that is positive charge picture … what about negative charge picture?

Electric field lines radiate outward from a positive charge - pretend there is a small positive test charge – which way would it want to go – that’s the direction of the field!

19Efield Physlet

Two charges – combine Electric Field Lines!

Can you find any “zeros” along the x axis in either figure?How might you change one of the scenarios to create zeros?

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Two unequal charges

Far away – larger charge dominates! (“net charge”)

Close up – can see how field lines affected

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Why study Motion of Point Charges inElectric Fields?

TV !!

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Q: The path of the electron will be a:A) Horizontally East B) Horizontally East then WestC) Diagonal line to the North D) Diagonal line to the South

Motion of a charged particle in an Electric Field – Scenario 1

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Motion of a charged particle in an Electric Field – Scenario 2

Q: The path of the electron will be a:A) Horizontally East then West B) Curve to the NorthEastC) Curve to the SouthEast D) Diagonal line to the

NEE) Diagonal line to the SE

blank next

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Horizontally launched charge in vertical electric field (projectile!)

Electric Dipoles – two equal magnitude, opposite sign charges – short distance apart

We consider the dipole charges as acting together (thus, think of an imaginary “bar” and the charges are on the ends – the bar can rotate if necessary, keeping the charges separated by a distance L)

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Torque on a dipole in an Electric Field

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Dipole in an Electric Field – in Equilibrium?

Q: The dipole will be in unstable equilibrium if :A) p is parallel to E B) p is perpendicular to EC) p is anti-parallel to E (opposite direction)D) a dipole can never be in equilibrium in an Electric field

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Dipole in Electric Field scenarios (assume equal vector lengths for p)

1) Which ones (if any) are in stable equilibrium? 2) Which ones (if any) are in unstable equilibrium?3) Which ones (if any) have torques pointing out of the board?4) Which ones (if any) have torques pointing into the board?5) Which one(s) has(have) the largest magnitude torque?6) Which figures (if any) are “identical”

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Miscellaneous problems

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Miscellaneous problems

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Electroscope problem (charged balloons demo)!!

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