- #1
momowoo
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So in a graph where V is a function of x, when the slope is negative what does that mean about the direction of the field along the x axis? What about when the slope is positive?
-- E/M conceptual question regarding electric potential
- Thread starter momowoo
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In summary, the direction of the field along the x-axis in a graph where V is a function of x depends on the slope of the potential graph. A positive slope corresponds to a negative field, pointing towards the -x axis (to the left), while a negative slope corresponds to a positive field, pointing towards the +x axis (to the right). This relationship is due to the field being related to the negative of the slope of the potential graph.
- #2
berkeman
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Welcome to the PF.momowoo said:So in a graph where V is a function of x, when the slope is negative what does that mean about the direction of the field along the x axis? What about when the slope is positive?
Can you think of a charge distribution that might cause that V(x) graph? You might also consider if conductors might be involved...
- #3
momowoo
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Would that be a hollow sphere?
- #4
berkeman
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That's not what I'm picturing, but perhaps it might work as well. But it would take multiple hollow concentric conducting spheres charged to different voltages, no?momowoo said:
- #5
Doc Al
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How does the field relate to the potential difference? Say you had a uniform field point to the right. Imagine placing a positive test charge in that field. Which way will the field push the charge? Will a positive test charge tend to move towards higher or lower potential?
- #6
momowoo
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towards lower potential
- #7
berkeman
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Can you sketch the concentric conducting shells example that you alluded to? Can you label the shells with their voltages to make that graph work?
- #8
Doc Al
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Exactly. So what does that tell you about your diagram?momowoo said:
- #9
momowoo
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ohhh so if the graph shows a positive slope then the test charge would be moving towards the positive charge and if its negative then it would be moving away?
- #10
Doc Al
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Where the graph shows a positive slope, the positive test charge would tend to move towards lower potential (to the left). So what direction must the field be in that region?momowoo said:
So how does the field direction depend on the slope of the potential graph?
- #11
momowoo
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How do you define field direction? Wouldn't saying left and right be arbitrary?
- #12
Doc Al
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Just specify the direction with respect to the x-axis given. ("To the right" corresponds to the +x direction, in this case.)momowoo said:
- #13
momowoo
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ohhhhh. So in that case, the region defined by the positive slope is probably to the left of a positive test charge. The area in which there is a constant V value is at the charge and then the negative slope would be to the right of the test charge because there is lower PE the larger the x value.
- #14
momowoo
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its like when x is equal to 0(the reference point) that is some distance to the left of the pos charge right?
- #15
Doc Al
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What's the direction of the field?
- #16
momowoo
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To the left?
- #17
momowoo
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So does this mean that a positive slope means moving to the left and neg slope means moving to the right?
- #18
Doc Al
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Yes. Where the potential rises to the right, the field points left.momowoo said:
- #19
momowoo
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THANK YOU SO MUCH FOR HELPING ME <3
- #20
Doc Al
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Yes. The field is related to the negative (opposite) of the slope of the potential graph. So where the slope is positive, the field is negative -- pointing to the -x axis (to the left, in this case). And where the slope is negative, the field is positive.momowoo said:
You are very welcome.momowoo said:
Related to -- E/M conceptual question regarding electric potential
1. What is electric potential?
Electric potential refers to the amount of electric potential energy per unit charge at a given point in an electric field. It is a measure of the electric potential energy a charged object would possess at a specific point in the electric field.
2. How is electric potential different from electric field?
While electric field measures the force exerted on a charged object at a specific point in the electric field, electric potential measures the potential energy that the charged object would possess at that same point. Electric potential is therefore a scalar quantity, while electric field is a vector quantity.
3. What is the unit of electric potential?
The unit of electric potential is volts (V), which is equivalent to joules per coulomb (J/C).
4. How is electric potential calculated?
Electric potential is calculated using the formula V = kQ/r, where V is the electric potential in volts, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), Q is the charge of the object in coulombs, and r is the distance from the object in meters.
5. What is the relationship between electric potential and electric potential energy?
Electric potential energy is the energy a charged object possesses due to its position in an electric field. It is directly proportional to the electric potential, with the equation U = qV, where U is the electric potential energy in joules, q is the charge of the object in coulombs, and V is the electric potential in volts.
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