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electric potential and work done

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PG1995

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Hi

Could you please help me with this query? Thank you.

Regards
PG
 

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Generally, signs are a matter of convention and of definition. Here they phrased the question as "find the work done to move the charge". Hence, this implies that if an external source supplies energy and the charge gains energy, the work is positive. This is why they start the calculation off with a negative sign in the equation for work W.

In this case, the charge is positive and the fields is directed outward. Hence the integral itself is positive (as you say) and the charge naturally wants to move outward to a lower energy state. So, the charge is able to do work on something else, while it is moving outward.

However, if ρL is negative, the opposite is true, and work is done on the positive charge Q, when it moves outward.

If the question was "find the work done by the charge when it moves outward" the negative sign would not have been placed in the equation for work W.
 
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Thank you, Steve.

I'm sorry but I'm still missing the point.

You are correct that it's a matter of definition and convention. In two books I have used for physics course, the work done is taken to be positive when direction of displacement of charge and electric field is same and this positive works means that work is done by the field. Is that text using the definition the other around? Is that text taking work done to be negative when it's done by the field? Please guide me. Thanks.

Regards
PG
 
In two books I have used for physics course, the work done is taken to be positive when direction of displacement of charge and electric field is same and this positive works means that work is done by the field. Is that text using the definition the other around? Is that text taking work done to be negative when it's done by the field?

So, unless I'm misunderstanding you, the two definitions/conventions appear to be the same. The work done by the field is the same as the work done by the charge. It is positive by the definition you gave.

However, when you "find the work done to move the charge", it is of opposite sign from the work done by the charge/field.

Am I understanding you and the problem correctly?
 
Thank you.

However, when you "find the work done to move the charge", it is of opposite sign from the work done by the charge/field.

I understand it now. In short, if work done by the field or charge is positive then the work done to move the charge is negative and vice versa. But how would you explain this 'reverse' convention for "the work done to move the charge". For instance, when work done by charge is negative, it's simply because displacement and electric field have opposite directions. Let me know if my question is not clear. Thanks a lot.

Regards
PG
 
The reverse situation takes care of itself also once you define the work with a negative sign in front. If field and displacement are in the same direction, the work done to move the charge is negative, if they are in the opposite directions, the work done to move the charge is positive. The math takes care of everything once the convention is established and obeyed.
 
Thank you.

I think I get it now.

Hence, this implies that if an external source supplies energy and the charge gains energy, the work is positive. This is why they start the calculation off with a negative sign in the equation for work W.

So, that minus sign makes the math correct. For instance, assuming there is no minus sign then when work done by the charge is positive, the charge loses energy and some external source gains energy. So, without minus sign we have to infer that information ourselves.

Regards
PG
 
Your limits are wrong. Also, it is x, y and not dx,dy that the limits apply to. So x=1 and y=0 correspond and x=0.8 and y=0.6 correspond.

I see you noticed the typographical error in the book.
 
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Thank you, Steve.

I see you noticed the typographical error in the book.

Was there any?! I didn't notice any error.

Could you please also help me with these queries, Q1 and Q2? Thanks.

Regards
PG
 

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Basically, they are saying that a steady beam of moving electrons can sometimes be approximated as line of fixed charges. When we make this approximation, we are ignoring the magnetic field created by the current. Remember that moving charges are also a current. If we ignore the current and the associated magnetic field, we will still have an electric field due to the (seemingly) fixed electrons along the beam.

The current caused by a beam of electrons is significantly different than a current in a wire. In a wire, the charges move, but there is a charge balance because the moving electrons have the fixed nuclei with positive charge.

The difference means that a wire (with current) can be moved by a magnetic field, but not by an electric field, while an electron beam can be deflected by either a magnetic field or an electric field.
 
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