Q.Derive the expression for the force acting on a current carrying conductor placed in a uniform magnetic field. From the expression, deduce the condition when will the magnitude of the force be maximum and when will it be minimum. (3+1+1=5) OR Derive the expression for the force between two parallel linear conductors carrying current in the same direction. From the expression, define one ampere of current. How will the nature of the force be when the currents flow in the opposite direction? (3+1+1=5)

The magnetic force on a current-carrying wire depends on sin(theta) between the current direction and B; when the wire is parallel to B, that force is zero.

The force on a straight current-carrying conductor of length l in a uniform magnetic field B is given by

F = BIl*sin(theta)

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The magnetic force on a current-carrying wire is $F = BIL\sin\theta$, which is maximum when $\sin\theta = 1$, i.e. when the wire is perpendicular to $B$.

The force on a straight wire of length $L$ carrying current $I$ in a uniform field $B$ is

$F = BIL\sin\theta$

where $\theta$ is the angle between the current direction and $B$.

• If the wire is parallel to $B$ ($\theta = 0^\circ$), $\sin\theta = 0$, so $F = 0$. …

B has units tesla = Wb/m² = N/(A·m); newton/ampere² is NOT a unit of B.

Magnetic field B can be expressed as:

• tesla (T),
• weber/metre² (Wb/m²), since 1 T = 1 Wb/m²,
• newton/(ampere·metre), from F = BIL ⇒ B = F/(IL) = N/(A·m). …

The force on a current-carrying wire in a magnetic field depends on $\sin\theta$, which is maximum (=1) at θ = 90°.

A straight current-carrying conductor of length $L$ carrying current $I$, placed at angle $\theta$ to a uniform magnetic field $B$, experiences a force

$F = BIL\sin\theta$

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Summing the Lorentz force qv x B over all the moving charges in a straight conductor of length l carrying current I gives F = I l x B.

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The net force on any closed current loop in a uniform field is always zero.

For a closed circuit of current $I$ in a uniform magnetic field $\vec{B}$, the total force is

$\vec{F} = I \oint d\vec{l} \times \vec{B} = I\left(\oint d\vec{l}\right)\times \vec{B}$ …

Force on a current-carrying wire in a field is $F=Bil\sin\theta$; at $\theta=30^\circ$, $F=iBl/2$.

The magnetic force on a straight wire of length $l$ carrying current $i$ at angle $\theta$ to field $B$ is

$F=Bil\sin\theta.$ …

1 tesla = 1 weber per square metre, so 5 T = 5 Wb/m².

Magnetic flux density (magnetic field) B has the SI unit tesla. The tesla is defined from magnetic flux Φ = B·A, so B = Φ/A, giving:

$1\ \text{T} = 1\ \frac{\text{Wb}}{\text{m}^2}$

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Magnetic flux density B measures the strength of a magnetic field, defined either as flux per unit area or as force per unit (current × length).

Magnetic flux density (also simply called the magnetic field, B) at a point can be defined in two equivalent ways:

(1) As flux per unit area: B = dΦ/dA, the magnetic flux passing normally through a unit area held perpendicular to the field at that point.

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