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Physics Chapter 12 : Topic 12
Magnetic Flux Calculations
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The equation used to calculate magnetic flux through a surface perpendicular to a magnetic field is:
Reasoning: Magnetic flux is the product of magnetic flux density and area perpendicular to the field. $\Longrightarrow$ $\mathbf{\Phi = BA}$
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A magnetic field of $\mathbf{2T\ }$passes normally through an area of $\mathbf{3}\mathbf{\ m}^{\mathbf{2}}$. The magnetic flux is:
Reasoning: $\mathbf{\Phi = BA}$ $\Longrightarrow$ $\mathbf{\Phi = 2 \times 3 = 6\ Wb}$
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A surface has magnetic flux of $\mathbf{12\ Wb}$ in a magnetic field of $\mathbf{4\ T}$. Its area is:
Reasoning: $\mathbf{\Phi = BA}$ $\Longrightarrow$ $\mathbf{A =}$ $\frac{\mathbf{\Phi}}{\mathbf{B}}\mathbf{=}\frac{\mathbf{12}}{\mathbf{4}}\mathbf{= 3\ }\mathbf{m}^{\mathbf{2}}$
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A magnetic flux of $\mathbf{5\ Wb}$ passes through an area of $\mathbf{2}\mathbf{\ m}^{\mathbf{2}}$. The magnetic flux density is:
Reasoning: $\mathbf{B =}$ $\frac{\mathbf{\Phi}}{\mathbf{A}}$ $\Longrightarrow$ $\mathbf{B =}$ $\frac{\mathbf{5}}{\mathbf{2}}\mathbf{= 2.5\ T}$
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A coil has an area of $\mathbf{0.5\ }\mathbf{m}^{\mathbf{2}}$ placed perpendicular to a magnetic field of $\mathbf{4\ T}$. The flux through the coil is:
Reasoning: $\mathbf{\Phi = BA}$ $\Longrightarrow$ $\mathbf{\Phi = 4(0.5) = 2\ Wb}$
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If magnetic flux density is doubled while the area remains unchanged, the magnetic flux:
Reasoning: Magnetic flux is directly proportional to magnetic flux density.$\mathbf{\Phi \propto}$ $\mathbf{B}$
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If the area through which magnetic field passes is reduced to one-fourth, the magnetic flux becomes:
Reasoning: Since, $\mathbf{\Phi = BA}$ $\Longrightarrow$ Flux is directly proportional to area.
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A magnetic field of $\mathbf{0.8\ T}$ produces a flux of $\mathbf{4\ Wb}$. The area through which the field passes is:
Reasoning: $\mathbf{A =}$ $\frac{\mathbf{\Phi}}{\mathbf{B}}$ $\Longrightarrow$ $\mathbf{A =}$ $\frac{\mathbf{4}}{\mathbf{0.8}}\mathbf{= 5}\mathbf{\ m}^{\mathbf{2}}$
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A magnetic field of $\mathbf{6\ T}$ passes through an area of $\mathbf{0.25}\mathbf{\ m}^{\mathbf{2}}$. The flux is:
Reasoning: $\mathbf{\Phi = BA = 6(0.25) = 1.5\ Wb}$
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The magnetic flux through an area will be zero if:
Reasoning: When field lines are parallel to the surface, no magnetic field passes through the area.
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A rectangular surface has dimensions $\mathbf{2\ m \times 3\ m}$. It is placed perpendicular to a magnetic field of $\mathbf{5\ T}$. The flux is:
Reasoning: Area: $\mathbf{A = 2 \times 3 = 6\ }\mathbf{m}^{\mathbf{2}}$ ; Flux: $\mathbf{\Phi = BA = 5 \times 6 = 30\ Wb}$
12 / 25
If both magnetic field and area are increased by a factor of $\mathbf{2}$, the magnetic flux becomes:
Reasoning: $\mathbf{\Phi = BA}$ $\Longrightarrow$ $\mathbf{\Phi}^{\mathbf{'}}\mathbf{= (2B)(2A) = 4\ BA}$
13 / 25
A magnetic flux density of $\mathbf{10}^{\mathbf{- 3}}\mathbf{\ T}$ passes through an area of $\mathbf{100\ }\mathbf{m}^{\mathbf{2}}$. The flux is:
Reasoning: $\mathbf{\Phi = BA =}\mathbf{10}^{\mathbf{- 3}}\mathbf{\times 100 = 0.1\ Wb}$
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The value of magnetic flux is maximum when:
Reasoning: Maximum field lines pass through the surface when the surface is perpendicular to the magnetic field.
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A magnetic flux of $\mathbf{20\ Wb}$ is produced by a field of $\mathbf{5\ T}$. If the field is reduced to $\mathbf{2.5\ T}$, the new flux becomes:
Reasoning: The field is halved, so flux is halved. $\Longrightarrow$ $\mathbf{\Phi = 10\ Wb}$
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A coil has an area of $\mathbf{4\ }\mathbf{m}^{\mathbf{2}}$. If the magnetic flux through it is $\mathbf{16\ Wb}$, the magnetic flux density is:
Reasoning: $\mathbf{B =}$ $\frac{\mathbf{\Phi}}{\mathbf{A}}$ $\Longrightarrow$ $\mathbf{B =}$ $\frac{\mathbf{16}}{\mathbf{4}}\mathbf{= 4T}$
17 / 25
A student calculates magnetic flux using $\mathbf{\Phi = BA}$ but uses the total surface area instead of perpendicular area. The result will be:
Reasoning: Only the area perpendicular to magnetic field contributes to magnetic flux.
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The unit obtained from $\mathbf{(BA)}$ is:
Reasoning: $\mathbf{T \times}\mathbf{m}^{\mathbf{2}}\mathbf{= Wb}$
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A magnetic flux density remains constant while the area increases from $\mathbf{2\ m}^{\mathbf{2}}\mathbf{\ }$to $\mathbf{8\ m}^{\mathbf{2}}$. The flux becomes:
Reasoning: Area increases by factor. $\Longrightarrow$ $\mathbf{8\ /\ 2 = 4}$Therefore, flux increases four times.
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A magnetic field of $\mathbf{3\ T}$ passes through a circular area of radius $\mathbf{2\ m}$. The magnetic flux is:
Reasoning: Area of circle: $\mathbf{A = \pi}\mathbf{r}^{\mathbf{2}}\mathbf{= 4\pi}$Flux: $\mathbf{\Phi = BA = 3(4\pi) = 12\pi\ Wb}$
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If magnetic field direction changes but its magnitude and area remain constant, the magnetic flux:
Reasoning: Flux depends on the component of magnetic field perpendicular to the surface.
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A magnetic field of $\mathbf{2.5\ T}$ produces a flux of $\mathbf{5\ Wb}$. The required area is:
Reasoning: $\mathbf{A =}$ $\frac{\mathbf{\Phi}}{\mathbf{B}}$ $\Longrightarrow$ $\mathbf{A =}$ $\frac{\mathbf{5}}{\mathbf{2.5}}\mathbf{= 2}\mathbf{\ m}^{\mathbf{2}}$
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A magnetic field passing through a surface produces greater flux when:
Reasoning: Larger area allows more magnetic field lines to pass through it.
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The relationship $\mathbf{\Phi = BA}$ shows that magnetic flux is:
Reasoning: Increasing either $\mathbf{(B)}$ or $\mathbf{(A)}$ increases magnetic flux.
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A surface has zero magnetic flux even though a magnetic field exists because:
Reasoning: No field lines cross the surface when it is parallel to the field.
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