Shape of graph of torque vs angular displacement of galvanometer

In summary, the conversation discusses the relationship between torque and deflection in a galvanometer. It is determined by the current and magnetic field, but these can be disregarded and the same result can be achieved by manually twisting the coil. The magnitude of current and force applied by hand also affect the deflection. The deflection is related to the torque by a restoring torque from a spring, resulting in a linear graph. When the current is switched off, the needle returns to its original position due to the restoring torque from the spring.
  • #1
songoku
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Homework Statement
The diagram below shows galvanometer. A coil of wire is wound around a circular iron core which is placed between two magnets with circular surface such that the magnetic field (indicated by arrows) on the surface of iron core is directed perpendicularly onto the surface and of the same magnitude across the surface of iron core as shown in diagram.

When a constant current flows in the coil, the needle will be deflected to angle ##\theta## from the vertical direction. Sketch a graph to show the variation of torque ##\tau## on the soft iron core due to magnetic force acting on the coil with the angular displacement ##\theta## of the needle as the needle rotates from zero to ##\theta_0##. Explain
Relevant Equations
##\tau## = F . d
1616641905783.png


I know the torque will be zero when the deflection is zero and will be maximum when the angular displacement is θ0 but how to determine the exact shape of the graph?

Thanks
 
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  • #2
The question asks for the relationship between the torque and the deflection. Note that this has nothing to do with the current or the magnets. You could throw those away and twist the coil by hand and get the same result.
So what does control the relationship?
 
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  • #3
haruspex said:
The question asks for the relationship between the torque and the deflection. Note that this has nothing to do with the current or the magnets.
I thought the value of torque acting on the needle is somewhat related to current flowing through the galvanometer, maybe something like F = BIL and τ = F.d so the magnitude of current also affects the deflection.

If torque has nothing to do with current of magnetic field, how can torque on the needle produced?

You could throw those away and twist the coil by hand and get the same result. So what does control the relationship?
Maybe magnitude of force applied by hand?

Thanks
 
  • #4
songoku said:
I thought the value of torque acting on the needle is somewhat related to current flowing through the galvanometer, maybe something like F = BIL and τ = F.d so the magnitude of current also affects the deflection.

If torque has nothing to do with current of magnetic field, how can torque on the needle produced?Maybe magnitude of force applied by hand?

Thanks
The current creates the torque, and the torque creates the deflection. A given value of torque, no matter how provided, results in a certain deflection.
What determines how much deflection results from a given torque?
Hint: if the current is switched off what happens to the needle? Why does that happen?
 
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  • #5
haruspex said:
The current creates the torque, and the torque creates the deflection. A given value of torque, no matter how provided, results in a certain deflection.
What determines how much deflection results from a given torque?
Hint: if the current is switched off what happens to the needle? Why does that happen?
If the current is switched off, the needle will return to original position because there is restoring torque from spring. So it means that the deflection will be related to torque by spring.

Formula of restoring torque is: ##\tau = k.\theta## so the shape of the graph will be linear line similar to y = mx + c.

Am I correct? Thanks
 
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  • #6
songoku said:
If the current is switched off, the needle will return to original position because there is restoring torque from spring. So it means that the deflection will be related to torque by spring.

Formula of restoring torque is: ##\tau = k.\theta## so the shape of the graph will be linear line similar to y = mx + c.

Am I correct? Thanks
Yes.
 
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  • #7
Thank you very much haruspex
 

1. What is the relationship between torque and angular displacement of a galvanometer?

The shape of the graph of torque vs angular displacement of a galvanometer is typically a linear relationship. This means that as the angular displacement increases, the torque also increases proportionally.

2. What factors can affect the shape of this graph?

The shape of the graph can be affected by various factors such as the strength of the magnetic field, the size and shape of the galvanometer coil, and the material of the coil. Additionally, external factors like temperature and friction can also impact the shape of the graph.

3. How does the shape of this graph differ for different types of galvanometers?

The shape of the graph can differ for different types of galvanometers depending on their design and purpose. For example, a moving coil galvanometer may have a different shape than a moving iron galvanometer due to their different coil and magnet configurations.

4. Can the shape of the graph change over time?

Yes, the shape of the graph can change over time due to factors such as wear and tear of the galvanometer components, changes in the magnetic field strength, or changes in the environmental conditions. Regular calibration and maintenance can help ensure the accuracy and consistency of the graph shape.

5. How is the shape of this graph used in practical applications?

The shape of the graph is used to determine the sensitivity and accuracy of the galvanometer, as well as to calibrate and adjust the instrument for specific measurements. It is also used to analyze and interpret data collected from the galvanometer, such as in experiments involving electrical currents or magnetic fields.

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