The current in flowing along the path $A B C D$ of a cube (shown in the left figure) produces a magnetic field at the centre of cube of magnitude $B$. Dashed line depicts the non-conducting part of the cube. Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $D A E F G C D$, then the magnitude of magnetic field at the centre will be
KVPY 2018, Advanced
Download our app for free and get started
$(c)$ Given magnetic field due to a square loop $D A B C A$ at centre of cube is $B$.
Now, loop $D A E F G C D$ can be viewed as super position of three square loops as shown below.
So, net field at centre $=$ resultant of fields of these three loops
$\therefore \quad B _{\text {net }}=B \hat{ i }+B \hat{ j }-B \hat{ k }$
Magnitude of resultant field is
$\left| B _{\text {net }}\right|=\sqrt{B^{2}+B^{2}+B^{2}}=\sqrt{3} \cdot B$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A coil in the shape of an equilateral triangle of side $10\, {cm}$ lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field $20\, {mT}$. The torque acting on the coil when a current of $0.2\, {A}$ is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt{{x}} \times 10^{-5} \,{Nm}$. The value of ${x}$ is ..... .View Solution
- 2View SolutionIf a charged particle enters perpendicularly in the uniform magnetic field then
- 3Two very long, straight and insulated wires are kept at $90^o$ angle from each other In $xy -$ plane as shown in the figure. These wires carry current of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $P$ will beView Solution
- 4The deflection in moving coil galvanometer falls from $25$ divisions to $5$ division when a shunt of $24\ \Omega$ is applied. The resistance of galvanometer coil will be :View Solution
- 5The radius of a circular current carrying coil is $R$. At what distance from the centre of the coil on its axis, the intensity of magnetic field will be $\frac{1}{2 \sqrt{2}}$ times that at the centre?View Solution
- 6Two circular concentric loops of radii $r_1 = 20\,cm$ and $r_2 = 30\,cm$ are placed in the $X, Y-$ plane as shown in the figure. A current $I = 7\,amp$ is flowing through them. The magnetic moment of this loop system isView Solution
- 7An infinitely long straight conductor $AB$ is fixed and a current is passed through it. Another movable straight wire $CD$ of finite length and carrying current is held perpendicular to it and released. Neglect weight of the wireView Solution
- 8A galvanometer has a resistance of $25\, ohm$ and a maximum of $0.01\, A$ current can be passed through it. In order to change it into an ammeter of range $10\, A$, the shunt resistance required isView Solution
- 9A horizontal rod of mass $10\, gm$ and length $10\, cm$ is placed on a smooth plane inclined at an angle of $60^\circ $ with the horizontal, with the length of the rod parallel to the edge of the inclined plane. A uniform magnetic field of induction $B$ is applied vertically downwards. If the current through the rod is $1.73$ $ampere$, then the value of $B$ for which the rod remains stationary on the inclined plane is......$Tesla$View Solution
- 10Three long, straight and parallel wires carrying currents are arranged as shown in figure. The force experienced by $10\, cm$ length of wire $Q$ isView Solution
