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

153143
Above circuit shows a square loop ABCD with edge length $a$. The resistance of the wire $A B C$ is $r$ and that of ADC is $2 r$. The value of magnetic field at the centre $O$ of the loop assuming uniform wire is

1 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \odot$
2 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \otimes$
3 $\frac{\sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}} \odot$
4 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{\pi \mathrm{a}} \otimes$
Moving Charges & Magnetism

153144 A cylindrical conductor of radius $R$ is carrying a constant current. The plot of the magnitude of the magnetic field $B$ with the distance $d$ from the centre of the conductor, is correctly represented by the figure

1
2
3
4
Moving Charges & Magnetism

153145 If $B_{C}$ is the magnetic induction at the centre of a circular coil carrying current, then the magnetic induction at a point on the axis of the coil at a distance equal to the radius of the coil is

1 $\frac{B_{c}}{2 \sqrt{2}}$
2 $\frac{B_{c}}{2}$
3 $\frac{B_{c}}{4}$
4 $\frac{\mathrm{B}_{\mathrm{c}}}{\sqrt{2}}$
5 $\frac{B_{c}}{8}$
Moving Charges & Magnetism

153146 The magnetic field of a given length of wire for single turn coil at its center is ' $B$ ' then its value for two turns coil for the same wire is

1 $\frac{B}{4}$
2 $\frac{B}{2}$
3 $4 \mathrm{~B}$
4 $2 \mathrm{~B}$
Moving Charges & Magnetism

153148 Five wire having currents $I_{1}=1 \mathrm{~A}, I_{2}=2 \mathrm{~A}, I_{3}=$ $3 \mathrm{~A}, \mathrm{I}_{4}=1 \mathrm{~A}$ and $\mathrm{I}_{5}=4 \mathrm{~A}$
cut the page perpendicularly at points. $1,2,3,4$ and 5. The value of line integral of $\vec{B}$ around the dotted closed path is $\left(\right.$ i.e. $\left.\int \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{dl}}\right)$ is

1 0
2 $\mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
3 $2 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
4 $4 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
Moving Charges & Magnetism

153143
Above circuit shows a square loop ABCD with edge length $a$. The resistance of the wire $A B C$ is $r$ and that of ADC is $2 r$. The value of magnetic field at the centre $O$ of the loop assuming uniform wire is

1 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \odot$
2 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \otimes$
3 $\frac{\sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}} \odot$
4 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{\pi \mathrm{a}} \otimes$
Moving Charges & Magnetism

153144 A cylindrical conductor of radius $R$ is carrying a constant current. The plot of the magnitude of the magnetic field $B$ with the distance $d$ from the centre of the conductor, is correctly represented by the figure

1
2
3
4
Moving Charges & Magnetism

153145 If $B_{C}$ is the magnetic induction at the centre of a circular coil carrying current, then the magnetic induction at a point on the axis of the coil at a distance equal to the radius of the coil is

1 $\frac{B_{c}}{2 \sqrt{2}}$
2 $\frac{B_{c}}{2}$
3 $\frac{B_{c}}{4}$
4 $\frac{\mathrm{B}_{\mathrm{c}}}{\sqrt{2}}$
5 $\frac{B_{c}}{8}$
Moving Charges & Magnetism

153146 The magnetic field of a given length of wire for single turn coil at its center is ' $B$ ' then its value for two turns coil for the same wire is

1 $\frac{B}{4}$
2 $\frac{B}{2}$
3 $4 \mathrm{~B}$
4 $2 \mathrm{~B}$
Moving Charges & Magnetism

153148 Five wire having currents $I_{1}=1 \mathrm{~A}, I_{2}=2 \mathrm{~A}, I_{3}=$ $3 \mathrm{~A}, \mathrm{I}_{4}=1 \mathrm{~A}$ and $\mathrm{I}_{5}=4 \mathrm{~A}$
cut the page perpendicularly at points. $1,2,3,4$ and 5. The value of line integral of $\vec{B}$ around the dotted closed path is $\left(\right.$ i.e. $\left.\int \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{dl}}\right)$ is

1 0
2 $\mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
3 $2 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
4 $4 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
Moving Charges & Magnetism

153143
Above circuit shows a square loop ABCD with edge length $a$. The resistance of the wire $A B C$ is $r$ and that of ADC is $2 r$. The value of magnetic field at the centre $O$ of the loop assuming uniform wire is

1 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \odot$
2 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \otimes$
3 $\frac{\sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}} \odot$
4 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{\pi \mathrm{a}} \otimes$
Moving Charges & Magnetism

153144 A cylindrical conductor of radius $R$ is carrying a constant current. The plot of the magnitude of the magnetic field $B$ with the distance $d$ from the centre of the conductor, is correctly represented by the figure

1
2
3
4
Moving Charges & Magnetism

153145 If $B_{C}$ is the magnetic induction at the centre of a circular coil carrying current, then the magnetic induction at a point on the axis of the coil at a distance equal to the radius of the coil is

1 $\frac{B_{c}}{2 \sqrt{2}}$
2 $\frac{B_{c}}{2}$
3 $\frac{B_{c}}{4}$
4 $\frac{\mathrm{B}_{\mathrm{c}}}{\sqrt{2}}$
5 $\frac{B_{c}}{8}$
Moving Charges & Magnetism

153146 The magnetic field of a given length of wire for single turn coil at its center is ' $B$ ' then its value for two turns coil for the same wire is

1 $\frac{B}{4}$
2 $\frac{B}{2}$
3 $4 \mathrm{~B}$
4 $2 \mathrm{~B}$
Moving Charges & Magnetism

153148 Five wire having currents $I_{1}=1 \mathrm{~A}, I_{2}=2 \mathrm{~A}, I_{3}=$ $3 \mathrm{~A}, \mathrm{I}_{4}=1 \mathrm{~A}$ and $\mathrm{I}_{5}=4 \mathrm{~A}$
cut the page perpendicularly at points. $1,2,3,4$ and 5. The value of line integral of $\vec{B}$ around the dotted closed path is $\left(\right.$ i.e. $\left.\int \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{dl}}\right)$ is

1 0
2 $\mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
3 $2 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
4 $4 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
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Moving Charges & Magnetism

153143
Above circuit shows a square loop ABCD with edge length $a$. The resistance of the wire $A B C$ is $r$ and that of ADC is $2 r$. The value of magnetic field at the centre $O$ of the loop assuming uniform wire is

1 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \odot$
2 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \otimes$
3 $\frac{\sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}} \odot$
4 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{\pi \mathrm{a}} \otimes$
Moving Charges & Magnetism

153144 A cylindrical conductor of radius $R$ is carrying a constant current. The plot of the magnitude of the magnetic field $B$ with the distance $d$ from the centre of the conductor, is correctly represented by the figure

1
2
3
4
Moving Charges & Magnetism

153145 If $B_{C}$ is the magnetic induction at the centre of a circular coil carrying current, then the magnetic induction at a point on the axis of the coil at a distance equal to the radius of the coil is

1 $\frac{B_{c}}{2 \sqrt{2}}$
2 $\frac{B_{c}}{2}$
3 $\frac{B_{c}}{4}$
4 $\frac{\mathrm{B}_{\mathrm{c}}}{\sqrt{2}}$
5 $\frac{B_{c}}{8}$
Moving Charges & Magnetism

153146 The magnetic field of a given length of wire for single turn coil at its center is ' $B$ ' then its value for two turns coil for the same wire is

1 $\frac{B}{4}$
2 $\frac{B}{2}$
3 $4 \mathrm{~B}$
4 $2 \mathrm{~B}$
Moving Charges & Magnetism

153148 Five wire having currents $I_{1}=1 \mathrm{~A}, I_{2}=2 \mathrm{~A}, I_{3}=$ $3 \mathrm{~A}, \mathrm{I}_{4}=1 \mathrm{~A}$ and $\mathrm{I}_{5}=4 \mathrm{~A}$
cut the page perpendicularly at points. $1,2,3,4$ and 5. The value of line integral of $\vec{B}$ around the dotted closed path is $\left(\right.$ i.e. $\left.\int \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{dl}}\right)$ is

1 0
2 $\mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
3 $2 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
4 $4 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
Moving Charges & Magnetism

153143
Above circuit shows a square loop ABCD with edge length $a$. The resistance of the wire $A B C$ is $r$ and that of ADC is $2 r$. The value of magnetic field at the centre $O$ of the loop assuming uniform wire is

1 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \odot$
2 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{3 \pi \mathrm{a}} \otimes$
3 $\frac{\sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}} \odot$
4 $\frac{\sqrt{2} \mu_{\mathrm{o}} \mathrm{i}}{\pi \mathrm{a}} \otimes$
Moving Charges & Magnetism

153144 A cylindrical conductor of radius $R$ is carrying a constant current. The plot of the magnitude of the magnetic field $B$ with the distance $d$ from the centre of the conductor, is correctly represented by the figure

1
2
3
4
Moving Charges & Magnetism

153145 If $B_{C}$ is the magnetic induction at the centre of a circular coil carrying current, then the magnetic induction at a point on the axis of the coil at a distance equal to the radius of the coil is

1 $\frac{B_{c}}{2 \sqrt{2}}$
2 $\frac{B_{c}}{2}$
3 $\frac{B_{c}}{4}$
4 $\frac{\mathrm{B}_{\mathrm{c}}}{\sqrt{2}}$
5 $\frac{B_{c}}{8}$
Moving Charges & Magnetism

153146 The magnetic field of a given length of wire for single turn coil at its center is ' $B$ ' then its value for two turns coil for the same wire is

1 $\frac{B}{4}$
2 $\frac{B}{2}$
3 $4 \mathrm{~B}$
4 $2 \mathrm{~B}$
Moving Charges & Magnetism

153148 Five wire having currents $I_{1}=1 \mathrm{~A}, I_{2}=2 \mathrm{~A}, I_{3}=$ $3 \mathrm{~A}, \mathrm{I}_{4}=1 \mathrm{~A}$ and $\mathrm{I}_{5}=4 \mathrm{~A}$
cut the page perpendicularly at points. $1,2,3,4$ and 5. The value of line integral of $\vec{B}$ around the dotted closed path is $\left(\right.$ i.e. $\left.\int \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{dl}}\right)$ is

1 0
2 $\mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
3 $2 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$
4 $4 \mu_{\mathrm{o}} \mathrm{Wb} \cdot \mathrm{m}^{-1}$