• Physicslearner500039
In summary, the conversation discusses the equations for emf and mutual inductance, as well as the confusion regarding the area of a rotated coil and the use of Latex symbols in the homework statement. The understanding is clarified that the figure is a cutaway and the coils are actually meant to be complete circular coils. The conversation also clarifies that the situation being discussed involves two neighboring coils with axes parallel, then one is rotated 90 degrees, and the mutual inductance is discussed in terms of the two coils' fluxes.
Physicslearner500039
Homework Statement
In if coil 2 is turned so that its axis is vertical, does the mutual inductance increase or decrease? Explain.
Relevant Equations
emf = ##\frac {-N_{2} {d\phi}_{B2}} {dt}## ## M_{21} = \frac {{N_2}{\phi}_{B2}} {i_1}##
emf = ##\frac {-N_{2} {d\phi}_{B2}} {dt}## ## M_{21} = \frac {{N_2}{\phi}_{B2}} {i_1}## are the equations

This is the original position, now the coil 2 is moved so the axis is perpendicular. The flux ##{\phi}_{B2}## due to i1 is the amount of flux cutting the coil 2 due to change in current i1. My answer is 0, since no flux cuts the Coil 2 in 90 degrees position. Is it correct? My main confusion is with respect to the area of the coil. How to consider it? i do not see the coil 2 as closed circuit it is open loop. So, what will be the area. Please advise.

Note: One another problem is i cannot preview the Homework statement and the Relevant Equations section. I have a workaround for the equations section, but still not sure if latex symbols work for the Homework statement. Please advise.

Physicslearner500039 said:
My answer is 0, since no flux cuts the Coil 2 in 90 degrees position. Is it correct?
Hi. You are correct. There is (almost) zero flux through rotated coil-2. I say 'almost' because the coil has finite thickness and is spiral-wound which means a *very* small amount of flux cuts the coil - we can usually treat it as zero.
My main confusion is with respect to the area of the coil. How to consider it? i do not see the coil 2 as closed circuit it is open loop. So, what will be the area.
I'm not sure I understand the question. But see if this helps.

Visualise the flux and area as you have done here. You can then 'see' if flux passes through the coil, rather than being parallel to the coil's plane.

Mathematically, you multiply the *component* of flux perpendicular to the area (i.e. parallel to the area's normal) by the area.

For example, for area A with its normal at angle θ to uniform field B, the flux through the area is Φ = ABcosθ (which is zero if θ = 90º).
not sure if latex symbols work for the Homework statement.
Sorry, can't help with that.

TSny
When rotated 90 Degrees

Physicslearner500039 said:
My main confusion is with respect to the area of the coil. How to consider it? i do not see the coil 2 as closed circuit it is open loop. So, what will be the area.
I'm not sure, but I'm wondering if the figure is misleading you. The figure does not show the entire coils. The figure is a "cutaway" figure. The coils are complete circular coils.

I agree with TSNy (#4). The coils are meant to be omplete circular ones (or they cannot be called 'coils'!). The diagram is simply a cut-away schematic.

If they were actual open half-coils as shown, there could be no current through either and the question wouldn't make sense.

I interpret this as 2 neighboring coils with axes parallel, then one is rotated 90 deg. so that now the axes are mutually perpendicular.

In which case, what is mutual inductance in terms of the two coils' fluxes?

## 1. What is mutual inductance?

Mutual inductance is a phenomenon in which a changing current in one circuit induces a voltage in a nearby circuit. It is a measure of the ability of two circuits to influence each other's magnetic fields.

## 2. How is mutual inductance calculated?

Mutual inductance is calculated using the equation M = k * √(L1 * L2), where M is the mutual inductance, k is the coefficient of coupling, and L1 and L2 are the inductances of the two circuits.

## 3. What factors affect mutual inductance?

The factors that affect mutual inductance include the number of turns in the coils, the distance between the coils, the shape and size of the coils, and the material of the cores. Additionally, the orientation of the coils and the frequency of the current also play a role.

## 4. How does mutual inductance relate to self-inductance?

Mutual inductance and self-inductance are closely related. Self-inductance is the measure of the ability of a circuit to produce a magnetic field in response to a changing current, while mutual inductance is the measure of the ability of two circuits to influence each other's magnetic fields. Both are dependent on the inductance of the circuit and the current flowing through it.

## 5. What are some practical applications of mutual inductance?

Mutual inductance has many practical applications, such as in transformers, which are used to step up or step down voltage in power distribution systems. It is also used in wireless power transfer, induction heating, and inductive sensors, among others.

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