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

153196 A part of a long wire carrying a current $i$ is bent into a circle of radius $r$ as shown in figure. the net magnetic field at the centre $O$ of the circular loop is

1 $\frac{\mu_{0} \mathrm{i}}{4 \mathrm{r}}$
2 $\frac{\mu_{0} \mathrm{i}}{2 \mathrm{r}}$
3 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(\pi+1)$
4 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(\pi-1)$
Moving Charges & Magnetism

153197 To measured a magnetic field between the magnetic poles of a loud speaker, a small coil having 30 turns and $2.5 \mathrm{~cm}^{2}$ area is placed perpendicular to the field and removed immediately. If the total charge flown though the coil is $7.5 \times 10^{-3} \mathrm{C}$ and the total resistance of wire and galvanometer is $0.3 \Omega$, then the magnitude of the magnetic field is

1 $0.03 \mathrm{~T}$
2 $0.3 \mathrm{~T}$
3 $3 \mathrm{~T}$
4 $3 \times 10^{2} \mathrm{~T}$
Moving Charges & Magnetism

153198 The magnetic field at the centre $C$ of the arrangement shown in figure is

1 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(1+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{4 \pi \mathrm{r}}(1+\pi)$
3 $\frac{\mu_{0} \mathrm{i}}{\pi \mathrm{r}}(1+\pi)$
4 $\frac{\mu_{0} \mathrm{i}}{\mathrm{r}}(1+\pi)$
Moving Charges & Magnetism

153199 A circular loop and an infinitely long straight conductor carry equal currents, as shown in the figure. The net magnetic field at the cetnre of the loop is $B_{1}$, when the current in the loop is clockwise and $B_{2}$ when the current in the loop is anti-clockwise.

Then, $\frac{B_{1}}{B_{2}}$ is

1 $\frac{15}{29}$
2 $\frac{13}{15}$
3 $\frac{13}{17}$
4 $\frac{17}{19}$
Moving Charges & Magnetism

153196 A part of a long wire carrying a current $i$ is bent into a circle of radius $r$ as shown in figure. the net magnetic field at the centre $O$ of the circular loop is

1 $\frac{\mu_{0} \mathrm{i}}{4 \mathrm{r}}$
2 $\frac{\mu_{0} \mathrm{i}}{2 \mathrm{r}}$
3 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(\pi+1)$
4 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(\pi-1)$
Moving Charges & Magnetism

153197 To measured a magnetic field between the magnetic poles of a loud speaker, a small coil having 30 turns and $2.5 \mathrm{~cm}^{2}$ area is placed perpendicular to the field and removed immediately. If the total charge flown though the coil is $7.5 \times 10^{-3} \mathrm{C}$ and the total resistance of wire and galvanometer is $0.3 \Omega$, then the magnitude of the magnetic field is

1 $0.03 \mathrm{~T}$
2 $0.3 \mathrm{~T}$
3 $3 \mathrm{~T}$
4 $3 \times 10^{2} \mathrm{~T}$
Moving Charges & Magnetism

153198 The magnetic field at the centre $C$ of the arrangement shown in figure is

1 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(1+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{4 \pi \mathrm{r}}(1+\pi)$
3 $\frac{\mu_{0} \mathrm{i}}{\pi \mathrm{r}}(1+\pi)$
4 $\frac{\mu_{0} \mathrm{i}}{\mathrm{r}}(1+\pi)$
Moving Charges & Magnetism

153199 A circular loop and an infinitely long straight conductor carry equal currents, as shown in the figure. The net magnetic field at the cetnre of the loop is $B_{1}$, when the current in the loop is clockwise and $B_{2}$ when the current in the loop is anti-clockwise.

Then, $\frac{B_{1}}{B_{2}}$ is

1 $\frac{15}{29}$
2 $\frac{13}{15}$
3 $\frac{13}{17}$
4 $\frac{17}{19}$
Moving Charges & Magnetism

153196 A part of a long wire carrying a current $i$ is bent into a circle of radius $r$ as shown in figure. the net magnetic field at the centre $O$ of the circular loop is

1 $\frac{\mu_{0} \mathrm{i}}{4 \mathrm{r}}$
2 $\frac{\mu_{0} \mathrm{i}}{2 \mathrm{r}}$
3 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(\pi+1)$
4 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(\pi-1)$
Moving Charges & Magnetism

153197 To measured a magnetic field between the magnetic poles of a loud speaker, a small coil having 30 turns and $2.5 \mathrm{~cm}^{2}$ area is placed perpendicular to the field and removed immediately. If the total charge flown though the coil is $7.5 \times 10^{-3} \mathrm{C}$ and the total resistance of wire and galvanometer is $0.3 \Omega$, then the magnitude of the magnetic field is

1 $0.03 \mathrm{~T}$
2 $0.3 \mathrm{~T}$
3 $3 \mathrm{~T}$
4 $3 \times 10^{2} \mathrm{~T}$
Moving Charges & Magnetism

153198 The magnetic field at the centre $C$ of the arrangement shown in figure is

1 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(1+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{4 \pi \mathrm{r}}(1+\pi)$
3 $\frac{\mu_{0} \mathrm{i}}{\pi \mathrm{r}}(1+\pi)$
4 $\frac{\mu_{0} \mathrm{i}}{\mathrm{r}}(1+\pi)$
Moving Charges & Magnetism

153199 A circular loop and an infinitely long straight conductor carry equal currents, as shown in the figure. The net magnetic field at the cetnre of the loop is $B_{1}$, when the current in the loop is clockwise and $B_{2}$ when the current in the loop is anti-clockwise.

Then, $\frac{B_{1}}{B_{2}}$ is

1 $\frac{15}{29}$
2 $\frac{13}{15}$
3 $\frac{13}{17}$
4 $\frac{17}{19}$
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Moving Charges & Magnetism

153196 A part of a long wire carrying a current $i$ is bent into a circle of radius $r$ as shown in figure. the net magnetic field at the centre $O$ of the circular loop is

1 $\frac{\mu_{0} \mathrm{i}}{4 \mathrm{r}}$
2 $\frac{\mu_{0} \mathrm{i}}{2 \mathrm{r}}$
3 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(\pi+1)$
4 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(\pi-1)$
Moving Charges & Magnetism

153197 To measured a magnetic field between the magnetic poles of a loud speaker, a small coil having 30 turns and $2.5 \mathrm{~cm}^{2}$ area is placed perpendicular to the field and removed immediately. If the total charge flown though the coil is $7.5 \times 10^{-3} \mathrm{C}$ and the total resistance of wire and galvanometer is $0.3 \Omega$, then the magnitude of the magnetic field is

1 $0.03 \mathrm{~T}$
2 $0.3 \mathrm{~T}$
3 $3 \mathrm{~T}$
4 $3 \times 10^{2} \mathrm{~T}$
Moving Charges & Magnetism

153198 The magnetic field at the centre $C$ of the arrangement shown in figure is

1 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(1+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{4 \pi \mathrm{r}}(1+\pi)$
3 $\frac{\mu_{0} \mathrm{i}}{\pi \mathrm{r}}(1+\pi)$
4 $\frac{\mu_{0} \mathrm{i}}{\mathrm{r}}(1+\pi)$
Moving Charges & Magnetism

153199 A circular loop and an infinitely long straight conductor carry equal currents, as shown in the figure. The net magnetic field at the cetnre of the loop is $B_{1}$, when the current in the loop is clockwise and $B_{2}$ when the current in the loop is anti-clockwise.

Then, $\frac{B_{1}}{B_{2}}$ is

1 $\frac{15}{29}$
2 $\frac{13}{15}$
3 $\frac{13}{17}$
4 $\frac{17}{19}$