Electric fields Help Please

Hey,

I am literally confused over questions like these (multiple choice on AQA) :

1. The distances between two point charges are +8.0nC and +2.0nC is 60 mm.
The resultant electric field is zero, how far is this point from the +8.0nC ?
A - 20
B - 25
C - 40
D - 45

Similarly

2. The distances between two point charges are +4.0nC and -16.0nC is 120 mm.
The resultant electric field is zero, how far is this point from the +4.0nC ?
A - 24
B - 40
C - 80
D - 96
(distances are in mm)

Thanks in advance :smile:

(if possible please make a detailed explanation as I have read other similar post which all confuse me :s-smilie:

)

Reply 1

uberteknik

21

Original post by ssargithan

Hey,

I am literally confused over questions like these (multiple choice on AQA) :

1. The distances between two point charges are +8.0nC and +2.0nC is 60 mm.
The resultant electric field is zero, how far is this point from the +8.0nC ?
A - 20
B - 25
C - 40
D - 45

Similarly

2. The distances between two point charges are +4.0nC and -16.0nC is 120 mm.
The resultant electric field is zero, how far is this point from the +4.0nC ?
A - 24
B - 40
C - 80
D - 96
(distances are in mm)

Thanks in advance :smile:

(if possible please make a detailed explanation as I have read other similar post which all confuse me :s-smilie:

)

With questions like these, you always need to refer to a 'test charge' of 1 coulomb placed at the point in question.

The two +ve charges will create a repulsive force mutually between them.

Coulombs law (electric field strength) gives the relationship between the force acting on a 1 coulomb test charge and the point charge in question:

F = \frac{kQq}{r^2}

where Q = 1 coulomb then

E = \frac{kq}{r^2}

where

k = \frac{1}{4 \Pi \epsilon_o}

Because the forces are both repulsive and follow an inverse square distance relationship, there will be a position between the two charges where the forces are balanced. i.e.the push from one charge is the same as the push from the second charge acting in the opposite direction.

At that point the electric field strength is zero.

The problem is tackled by defining the distance between one of the charges and the zero position as x.

The zero position from the other charge is then (6 - x).

And the forces will be balanced when:

\frac{2nC}{x^2} = \frac{8nC}{(6 -x)^2}

This can be written as a quadratic to solve for x.

NB, the units (mm distance and nC charges) can be reduced to integers to make the working easier.

Alternately, when given multiple choice answers, you can first use inspection to work out the force produced by the larger charge will move the zero electric potential position closer to the smaller charge. Then eliminate answers (in this case a and b), and finally plug numbers in to the force equation to which will show you which answer balances.

Spoiler

(edited 9 years ago)

Reply 2

Stonebridge

13

What uber says above is perfectly true.
However, in a multiple choice test there is very little time available for each question. There is a much quicker way of finding the correct alternative in these types of question, where the values given for the charges are in a nice simple ratio that has a square root...

I explain how to do it here. Scroll down to find my post.

http://www.thestudentroom.co.uk/showthread.php?p=41062724

Reply 3

uberteknik

21

Original post by Stonebridge

What uber says above is perfectly true.
However, in a multiple choice test there is very little time available for each question. There is a much quicker way of finding the correct alternative in these types of question, where the values given for the charges are in a nice simple ratio that has a square root...

I explain how to do it here. Scroll down to find my post.

http://www.thestudentroom.co.uk/showthread.php?p=41062724

Thanks Stonebridge! I knew there was an easier way. lol. :colondollar:

Reply 4

Anonymous_0749

OP

15

Hey,

For the first one it works (both methods) but for the second question it does work ? I mean do I just ignore the minus.. if I do so it gives me 40 mm.... but the answer is 24mm?

Thanks

Reply 5

Stonebridge

13

Original post by ssargithan

Hey,

For the first one it works (both methods) but for the second question it does work ? I mean do I just ignore the minus.. if I do so it gives me 40 mm.... but the answer is 24mm?

Thanks

First of all check that the question is exactly right.
Is one plus and one minus?
Is it asking for electric field zero or electric potential zero?

Electric fields Help Please

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