(D) The charge $q = 1000e = 1000 \times 1.6 \times 10^{-19} \ C = 1.6 \times 10^{-16} \ C$. The frequency of rotation $f = 1 \ Hz$. The equivalent cur

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(D) The charge $q = 1000e = 1000 \times 1.6 \times 10^{-19} \ C = 1.6 \times 10^{-16} \ C$. The frequency of rotation $f = 1 \ Hz$. The equivalent current $I = qf = 1.6 \times 10^{-16} \times 1 = 1.6 \times 10^{-16} \ A$. The magnetic field at the center of a circular loop is $B = \frac{\mu_0 I}{2r}$. Given $B = x \mu_0$,where $x = 2 \times 10^{-16}$. So,$x \mu_0 = \frac{\mu_0 I}{2r} \implies x = \frac{I}{2r}$. Substituting the values: $2 \times 10^{-16} = \frac{1.6 \times 10^{-16}}{2r}$. $2 = \frac{0.8}{r} \implies r = \frac{0.8}{2} = 0.4 \ m$.

Class 12 Physics Moving Charges and Magnetism Biot-Savart's Law and its application

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$A$ particle carrying a charge equal to $1000$ times the charge on an electron is rotating at $1$ rotation per second in a circular path of radius $r \ m$. If the magnetic field produced at the centre of the path is $x$ times the permeability of vacuum $\mu_0$,the radius $r$ in $m$ is: $[e = 1.6 \times 10^{-19} \ C], [x = 2 \times 10^{-16}]$

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Moving Charges and Magnetism

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Biot-Savart's Law and its application

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$A$ current of $I$ $A$ is passed through a straight wire of length $2.0$ $m$. The magnetic field at a point in air at a distance of $3$ $m$ from either end of the wire and lying on the axis of the wire will be:

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An element $\Delta l = \Delta x \hat{i}$ is placed at the origin and carries a large current $I = 10 \; A$ (Figure). What is the magnetic field on the $y$-axis at a distance of $0.5 \; m$? Given $\Delta x = 1 \; cm$.

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$A$ current of $0.1\, A$ circulates around a coil of $100$ turns and having a radius equal to $5\, cm$. The magnetic field set up at the centre of the coil is $({\mu _0} = 4\pi \times {10^{ - 7}}\,T\cdot m/A)$.

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Two concentric circular coils of $10$ turns each are situated in the same plane. Their radii are $20 \, cm$ and $40 \, cm$ and they carry respectively $0.2 \, A$ and $0.3 \, A$ current in opposite directions. The magnetic field at the centre is $(\mu_0 = 4 \pi \times 10^{-7} \, T \cdot m/A)$

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$A$ battery is connected between two points $A$ and $B$ on the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $AB$ of the ring subtends an angle $\theta$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

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$A$ current of $I$ $A$ is passed through a straight wire of length $2.0$ $m$. The magnetic field at a point in air at a distance of $3$ $m$ from either end of the wire and lying on the axis of the wire will be:

An element $\Delta l = \Delta x \hat{i}$ is placed at the origin and carries a large current $I = 10 \; A$ (Figure). What is the magnetic field on the $y$-axis at a distance of $0.5 \; m$? Given $\Delta x = 1 \; cm$.

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$A$ battery is connected between two points $A$ and $B$ on the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $AB$ of the ring subtends an angle $\theta$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

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