00. Biot-Savart's Law and Magnetic Field, Lorentz Force
Moving Charges & Magnetism

153229 A non-conducting disc of radius $R$ has surface charge density which varies with distance from the centre as $\sigma(r)=\sigma_{0}\left[1+\sqrt{\frac{r}{R}}\right]$, where $\sigma_{0}$ is a constant. The disc rotates about its axis with angular velocity $\omega$. If $B$ is the magnitude of magnetic induction at the centre, then $\frac{B}{\mu_{0} \sigma_{0} \omega R}$ will be

1 $\frac{3}{4}$
2 $\frac{4}{5}$
3 $\frac{5}{6}$
4 $\frac{6}{7}$
Moving Charges & Magnetism

153231 A unit negative charge with mass $M$ resides at the mid-point of the straight line of length $2 a$ adjoining two fixed charges of magnitude $+Q$ each. If it is given a very small displacement $x(x$ $\lta$ ) in a direction perpendicular to the straight line, it will

1 come back to its original position and stay there
2 execute oscillations with frequency
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Q}}{2 \pi \varepsilon_{0} \mathrm{Ma}^{3}}}$
3 fly to infinity
4 execute oscillations with frequency
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Q}}{4 \pi \varepsilon_{0} \mathrm{M} a^{2}}}$
Moving Charges & Magnetism

153233 The magnetic induction at the centre of a current carrying circular coil of radius $8 \mathrm{~cm}$ is $6 \sqrt{6}$ times the magnetic induction at a point on its axis. Then the distance of the point from the centre of the coil in $\mathrm{cm}$ is $(\sqrt{5}=\mathbf{2 . 2 3 6})$

1 17.89
2 1.789
3 178.9
4 0.1789
Moving Charges & Magnetism

153235 Consider a metal ball of radius ' $r$ ' moving at a constant velocity ' $v$ ' in a uniform magnetic field of induction $\vec{B}$. Assuming that the direction of velocity forms an angle ' $\alpha$ ' with the direction of $\vec{B}$, the maximum potential difference between points on the ball is

1 $\mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
2 $|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
3 $2 \mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
4 $2 \mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \cos \alpha$
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Moving Charges & Magnetism

153229 A non-conducting disc of radius $R$ has surface charge density which varies with distance from the centre as $\sigma(r)=\sigma_{0}\left[1+\sqrt{\frac{r}{R}}\right]$, where $\sigma_{0}$ is a constant. The disc rotates about its axis with angular velocity $\omega$. If $B$ is the magnitude of magnetic induction at the centre, then $\frac{B}{\mu_{0} \sigma_{0} \omega R}$ will be

1 $\frac{3}{4}$
2 $\frac{4}{5}$
3 $\frac{5}{6}$
4 $\frac{6}{7}$
Moving Charges & Magnetism

153231 A unit negative charge with mass $M$ resides at the mid-point of the straight line of length $2 a$ adjoining two fixed charges of magnitude $+Q$ each. If it is given a very small displacement $x(x$ $\lta$ ) in a direction perpendicular to the straight line, it will

1 come back to its original position and stay there
2 execute oscillations with frequency
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Q}}{2 \pi \varepsilon_{0} \mathrm{Ma}^{3}}}$
3 fly to infinity
4 execute oscillations with frequency
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Q}}{4 \pi \varepsilon_{0} \mathrm{M} a^{2}}}$
Moving Charges & Magnetism

153233 The magnetic induction at the centre of a current carrying circular coil of radius $8 \mathrm{~cm}$ is $6 \sqrt{6}$ times the magnetic induction at a point on its axis. Then the distance of the point from the centre of the coil in $\mathrm{cm}$ is $(\sqrt{5}=\mathbf{2 . 2 3 6})$

1 17.89
2 1.789
3 178.9
4 0.1789
Moving Charges & Magnetism

153235 Consider a metal ball of radius ' $r$ ' moving at a constant velocity ' $v$ ' in a uniform magnetic field of induction $\vec{B}$. Assuming that the direction of velocity forms an angle ' $\alpha$ ' with the direction of $\vec{B}$, the maximum potential difference between points on the ball is

1 $\mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
2 $|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
3 $2 \mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
4 $2 \mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \cos \alpha$
Moving Charges & Magnetism

153229 A non-conducting disc of radius $R$ has surface charge density which varies with distance from the centre as $\sigma(r)=\sigma_{0}\left[1+\sqrt{\frac{r}{R}}\right]$, where $\sigma_{0}$ is a constant. The disc rotates about its axis with angular velocity $\omega$. If $B$ is the magnitude of magnetic induction at the centre, then $\frac{B}{\mu_{0} \sigma_{0} \omega R}$ will be

1 $\frac{3}{4}$
2 $\frac{4}{5}$
3 $\frac{5}{6}$
4 $\frac{6}{7}$
Moving Charges & Magnetism

153231 A unit negative charge with mass $M$ resides at the mid-point of the straight line of length $2 a$ adjoining two fixed charges of magnitude $+Q$ each. If it is given a very small displacement $x(x$ $\lta$ ) in a direction perpendicular to the straight line, it will

1 come back to its original position and stay there
2 execute oscillations with frequency
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Q}}{2 \pi \varepsilon_{0} \mathrm{Ma}^{3}}}$
3 fly to infinity
4 execute oscillations with frequency
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Q}}{4 \pi \varepsilon_{0} \mathrm{M} a^{2}}}$
Moving Charges & Magnetism

153233 The magnetic induction at the centre of a current carrying circular coil of radius $8 \mathrm{~cm}$ is $6 \sqrt{6}$ times the magnetic induction at a point on its axis. Then the distance of the point from the centre of the coil in $\mathrm{cm}$ is $(\sqrt{5}=\mathbf{2 . 2 3 6})$

1 17.89
2 1.789
3 178.9
4 0.1789
Moving Charges & Magnetism

153235 Consider a metal ball of radius ' $r$ ' moving at a constant velocity ' $v$ ' in a uniform magnetic field of induction $\vec{B}$. Assuming that the direction of velocity forms an angle ' $\alpha$ ' with the direction of $\vec{B}$, the maximum potential difference between points on the ball is

1 $\mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
2 $|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
3 $2 \mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
4 $2 \mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \cos \alpha$
Moving Charges & Magnetism

153229 A non-conducting disc of radius $R$ has surface charge density which varies with distance from the centre as $\sigma(r)=\sigma_{0}\left[1+\sqrt{\frac{r}{R}}\right]$, where $\sigma_{0}$ is a constant. The disc rotates about its axis with angular velocity $\omega$. If $B$ is the magnitude of magnetic induction at the centre, then $\frac{B}{\mu_{0} \sigma_{0} \omega R}$ will be

1 $\frac{3}{4}$
2 $\frac{4}{5}$
3 $\frac{5}{6}$
4 $\frac{6}{7}$
Moving Charges & Magnetism

153231 A unit negative charge with mass $M$ resides at the mid-point of the straight line of length $2 a$ adjoining two fixed charges of magnitude $+Q$ each. If it is given a very small displacement $x(x$ $\lta$ ) in a direction perpendicular to the straight line, it will

1 come back to its original position and stay there
2 execute oscillations with frequency
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Q}}{2 \pi \varepsilon_{0} \mathrm{Ma}^{3}}}$
3 fly to infinity
4 execute oscillations with frequency
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Q}}{4 \pi \varepsilon_{0} \mathrm{M} a^{2}}}$
Moving Charges & Magnetism

153233 The magnetic induction at the centre of a current carrying circular coil of radius $8 \mathrm{~cm}$ is $6 \sqrt{6}$ times the magnetic induction at a point on its axis. Then the distance of the point from the centre of the coil in $\mathrm{cm}$ is $(\sqrt{5}=\mathbf{2 . 2 3 6})$

1 17.89
2 1.789
3 178.9
4 0.1789
Moving Charges & Magnetism

153235 Consider a metal ball of radius ' $r$ ' moving at a constant velocity ' $v$ ' in a uniform magnetic field of induction $\vec{B}$. Assuming that the direction of velocity forms an angle ' $\alpha$ ' with the direction of $\vec{B}$, the maximum potential difference between points on the ball is

1 $\mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
2 $|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
3 $2 \mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \sin \alpha$
4 $2 \mathrm{r}|\overrightarrow{\mathrm{B}}||\overrightarrow{\mathrm{v}}| \cos \alpha$