Biot-Savart Law
PHXII04:MOVING CHARGES AND MAGNETISM

362531 Two similar coils of radius \(R\) and number of turns \(N\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\,\& \,I\sqrt 3 \) respectively. Find the magnetic field induction at the center of the coils.

1 \(\dfrac{2 \mu_{0} N I}{R}\)
2 \(\dfrac{3 \mu_{0} N I R}{2}\)
3 \(\dfrac{\mu_{0} N I R}{2}\)
4 \(\dfrac{\mu_{0} N I}{R}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362532 In the given figure, magnetic field at the center of ring \({(O)}\) is \({8 \sqrt{2} T}\). Now, it is turned through a \({90^{\circ}}\) angle about \({x x^{\prime}}\) axis, so that two semicircular parts are mutually perpendicular. Find the value of magnetic field (in \(T\,)\) at centre
supporting img

1 \({8 T}\)
2 \({16 T}\)
3 \({4 T}\)
4 \({24 T}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362533 A part of a long wire carrying a current 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
supporting img

1 \(\dfrac{\mu_{0} i}{4 r}\)
2 \(\dfrac{\mu_{0} i}{2 r}\)
3 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi+1)\)
4 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi-1)\)
PHXII04:MOVING CHARGES AND MAGNETISM

362534 Two concentric coils each of radius equal to \(2\,\pi \,cm\) are placed at right angles to each other. \(3\;A\) and \(4\;A\) are the current flowing in each coil, respectively. The magnetic induction (in \(Wb{m^{ - 2}}\)) at the centre of the coils will be (Take, \({\mu _0} = 4\pi \times {10^{ - 7}}\;Wb\,{A^{ - 1}}\;{m^{ - 1}}\)).

1 \(12 \times 10^{-5}\)
2 \(10^{-5}\)
3 \(5 \times 10^{-5}\)
4 \(7 \times 10^{-5}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362535 Two identical wires \(A\) and \(B\), each of length ' \(\ell\) ', carry the same current \(I\). Wire \(A\) is bent into a circle of radius \(R\) and wire \(B\) is bent to form a square of side ' \(a\) '. If \(B_{A}\) and \(B_{B}\) are the values of magnetic field at the centers of the circle and square respectively, then the ratio \(\dfrac{B_{A}}{B_{B}}\) is

1 \(\dfrac{\pi^{2}}{16 \sqrt{2}}\)
2 \(\dfrac{\pi^{2}}{16}\)
3 \(\dfrac{\pi^{2}}{8 \sqrt{2}}\)
4 \(\dfrac{\pi^{2}}{8}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362531 Two similar coils of radius \(R\) and number of turns \(N\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\,\& \,I\sqrt 3 \) respectively. Find the magnetic field induction at the center of the coils.

1 \(\dfrac{2 \mu_{0} N I}{R}\)
2 \(\dfrac{3 \mu_{0} N I R}{2}\)
3 \(\dfrac{\mu_{0} N I R}{2}\)
4 \(\dfrac{\mu_{0} N I}{R}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362532 In the given figure, magnetic field at the center of ring \({(O)}\) is \({8 \sqrt{2} T}\). Now, it is turned through a \({90^{\circ}}\) angle about \({x x^{\prime}}\) axis, so that two semicircular parts are mutually perpendicular. Find the value of magnetic field (in \(T\,)\) at centre
supporting img

1 \({8 T}\)
2 \({16 T}\)
3 \({4 T}\)
4 \({24 T}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362533 A part of a long wire carrying a current 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
supporting img

1 \(\dfrac{\mu_{0} i}{4 r}\)
2 \(\dfrac{\mu_{0} i}{2 r}\)
3 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi+1)\)
4 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi-1)\)
PHXII04:MOVING CHARGES AND MAGNETISM

362534 Two concentric coils each of radius equal to \(2\,\pi \,cm\) are placed at right angles to each other. \(3\;A\) and \(4\;A\) are the current flowing in each coil, respectively. The magnetic induction (in \(Wb{m^{ - 2}}\)) at the centre of the coils will be (Take, \({\mu _0} = 4\pi \times {10^{ - 7}}\;Wb\,{A^{ - 1}}\;{m^{ - 1}}\)).

1 \(12 \times 10^{-5}\)
2 \(10^{-5}\)
3 \(5 \times 10^{-5}\)
4 \(7 \times 10^{-5}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362535 Two identical wires \(A\) and \(B\), each of length ' \(\ell\) ', carry the same current \(I\). Wire \(A\) is bent into a circle of radius \(R\) and wire \(B\) is bent to form a square of side ' \(a\) '. If \(B_{A}\) and \(B_{B}\) are the values of magnetic field at the centers of the circle and square respectively, then the ratio \(\dfrac{B_{A}}{B_{B}}\) is

1 \(\dfrac{\pi^{2}}{16 \sqrt{2}}\)
2 \(\dfrac{\pi^{2}}{16}\)
3 \(\dfrac{\pi^{2}}{8 \sqrt{2}}\)
4 \(\dfrac{\pi^{2}}{8}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362531 Two similar coils of radius \(R\) and number of turns \(N\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\,\& \,I\sqrt 3 \) respectively. Find the magnetic field induction at the center of the coils.

1 \(\dfrac{2 \mu_{0} N I}{R}\)
2 \(\dfrac{3 \mu_{0} N I R}{2}\)
3 \(\dfrac{\mu_{0} N I R}{2}\)
4 \(\dfrac{\mu_{0} N I}{R}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362532 In the given figure, magnetic field at the center of ring \({(O)}\) is \({8 \sqrt{2} T}\). Now, it is turned through a \({90^{\circ}}\) angle about \({x x^{\prime}}\) axis, so that two semicircular parts are mutually perpendicular. Find the value of magnetic field (in \(T\,)\) at centre
supporting img

1 \({8 T}\)
2 \({16 T}\)
3 \({4 T}\)
4 \({24 T}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362533 A part of a long wire carrying a current 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
supporting img

1 \(\dfrac{\mu_{0} i}{4 r}\)
2 \(\dfrac{\mu_{0} i}{2 r}\)
3 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi+1)\)
4 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi-1)\)
PHXII04:MOVING CHARGES AND MAGNETISM

362534 Two concentric coils each of radius equal to \(2\,\pi \,cm\) are placed at right angles to each other. \(3\;A\) and \(4\;A\) are the current flowing in each coil, respectively. The magnetic induction (in \(Wb{m^{ - 2}}\)) at the centre of the coils will be (Take, \({\mu _0} = 4\pi \times {10^{ - 7}}\;Wb\,{A^{ - 1}}\;{m^{ - 1}}\)).

1 \(12 \times 10^{-5}\)
2 \(10^{-5}\)
3 \(5 \times 10^{-5}\)
4 \(7 \times 10^{-5}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362535 Two identical wires \(A\) and \(B\), each of length ' \(\ell\) ', carry the same current \(I\). Wire \(A\) is bent into a circle of radius \(R\) and wire \(B\) is bent to form a square of side ' \(a\) '. If \(B_{A}\) and \(B_{B}\) are the values of magnetic field at the centers of the circle and square respectively, then the ratio \(\dfrac{B_{A}}{B_{B}}\) is

1 \(\dfrac{\pi^{2}}{16 \sqrt{2}}\)
2 \(\dfrac{\pi^{2}}{16}\)
3 \(\dfrac{\pi^{2}}{8 \sqrt{2}}\)
4 \(\dfrac{\pi^{2}}{8}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362531 Two similar coils of radius \(R\) and number of turns \(N\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\,\& \,I\sqrt 3 \) respectively. Find the magnetic field induction at the center of the coils.

1 \(\dfrac{2 \mu_{0} N I}{R}\)
2 \(\dfrac{3 \mu_{0} N I R}{2}\)
3 \(\dfrac{\mu_{0} N I R}{2}\)
4 \(\dfrac{\mu_{0} N I}{R}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362532 In the given figure, magnetic field at the center of ring \({(O)}\) is \({8 \sqrt{2} T}\). Now, it is turned through a \({90^{\circ}}\) angle about \({x x^{\prime}}\) axis, so that two semicircular parts are mutually perpendicular. Find the value of magnetic field (in \(T\,)\) at centre
supporting img

1 \({8 T}\)
2 \({16 T}\)
3 \({4 T}\)
4 \({24 T}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362533 A part of a long wire carrying a current 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
supporting img

1 \(\dfrac{\mu_{0} i}{4 r}\)
2 \(\dfrac{\mu_{0} i}{2 r}\)
3 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi+1)\)
4 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi-1)\)
PHXII04:MOVING CHARGES AND MAGNETISM

362534 Two concentric coils each of radius equal to \(2\,\pi \,cm\) are placed at right angles to each other. \(3\;A\) and \(4\;A\) are the current flowing in each coil, respectively. The magnetic induction (in \(Wb{m^{ - 2}}\)) at the centre of the coils will be (Take, \({\mu _0} = 4\pi \times {10^{ - 7}}\;Wb\,{A^{ - 1}}\;{m^{ - 1}}\)).

1 \(12 \times 10^{-5}\)
2 \(10^{-5}\)
3 \(5 \times 10^{-5}\)
4 \(7 \times 10^{-5}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362535 Two identical wires \(A\) and \(B\), each of length ' \(\ell\) ', carry the same current \(I\). Wire \(A\) is bent into a circle of radius \(R\) and wire \(B\) is bent to form a square of side ' \(a\) '. If \(B_{A}\) and \(B_{B}\) are the values of magnetic field at the centers of the circle and square respectively, then the ratio \(\dfrac{B_{A}}{B_{B}}\) is

1 \(\dfrac{\pi^{2}}{16 \sqrt{2}}\)
2 \(\dfrac{\pi^{2}}{16}\)
3 \(\dfrac{\pi^{2}}{8 \sqrt{2}}\)
4 \(\dfrac{\pi^{2}}{8}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362531 Two similar coils of radius \(R\) and number of turns \(N\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\,\& \,I\sqrt 3 \) respectively. Find the magnetic field induction at the center of the coils.

1 \(\dfrac{2 \mu_{0} N I}{R}\)
2 \(\dfrac{3 \mu_{0} N I R}{2}\)
3 \(\dfrac{\mu_{0} N I R}{2}\)
4 \(\dfrac{\mu_{0} N I}{R}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362532 In the given figure, magnetic field at the center of ring \({(O)}\) is \({8 \sqrt{2} T}\). Now, it is turned through a \({90^{\circ}}\) angle about \({x x^{\prime}}\) axis, so that two semicircular parts are mutually perpendicular. Find the value of magnetic field (in \(T\,)\) at centre
supporting img

1 \({8 T}\)
2 \({16 T}\)
3 \({4 T}\)
4 \({24 T}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362533 A part of a long wire carrying a current 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
supporting img

1 \(\dfrac{\mu_{0} i}{4 r}\)
2 \(\dfrac{\mu_{0} i}{2 r}\)
3 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi+1)\)
4 \(\dfrac{\mu_{0} i}{2 \pi r}(\pi-1)\)
PHXII04:MOVING CHARGES AND MAGNETISM

362534 Two concentric coils each of radius equal to \(2\,\pi \,cm\) are placed at right angles to each other. \(3\;A\) and \(4\;A\) are the current flowing in each coil, respectively. The magnetic induction (in \(Wb{m^{ - 2}}\)) at the centre of the coils will be (Take, \({\mu _0} = 4\pi \times {10^{ - 7}}\;Wb\,{A^{ - 1}}\;{m^{ - 1}}\)).

1 \(12 \times 10^{-5}\)
2 \(10^{-5}\)
3 \(5 \times 10^{-5}\)
4 \(7 \times 10^{-5}\)
PHXII04:MOVING CHARGES AND MAGNETISM

362535 Two identical wires \(A\) and \(B\), each of length ' \(\ell\) ', carry the same current \(I\). Wire \(A\) is bent into a circle of radius \(R\) and wire \(B\) is bent to form a square of side ' \(a\) '. If \(B_{A}\) and \(B_{B}\) are the values of magnetic field at the centers of the circle and square respectively, then the ratio \(\dfrac{B_{A}}{B_{B}}\) is

1 \(\dfrac{\pi^{2}}{16 \sqrt{2}}\)
2 \(\dfrac{\pi^{2}}{16}\)
3 \(\dfrac{\pi^{2}}{8 \sqrt{2}}\)
4 \(\dfrac{\pi^{2}}{8}\)