Two coaxial solenoids $1$ and $2$ of the same length are set so that one is inside the other. The number of turns per unit length are ${n_1}$ and ${n_2}$. The currents ${i_1}$ and ${i_2}$ are flowing in opposite directions. The magnetic field inside the inner coil is zero. This is possible when
So ${n_1}{i_1} = {n_2}{i_2}$ or ${n_1} = {n_2}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\text{and}}\,\,\,{i_1} = {i_2}$
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The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_A=10 cm$ and $r_B=20 cm$ respectively are equal if: (Where $N _A, I _{ A }$ and $N _B, I _{ B }$ are number of turn and current of $A$ and $B$ respectively)
An infinitely long conductor $PQR$ is bent to from a right angle as shown. A current $I$ flows through $PQR$ . The magnetic field due to this current at the point $M$ is $H_1$ . Now, another infinitely long straight conductor $QS$ is connected at $Q$ so that the current in $PQ$ remaining unchanged. The magnetic field at $M$ is now $H_2$ . The ratio $H_1/H_2$ is given by
Two mutually perpendicular conductors carrying currents $I_1$ and $I_2$ lie in one plane. Locus of the point at which the magnetic induction is zero, is a
Consider three quantities $x = E/B,$ $y =\sqrt {1/{\mu _0}{\varepsilon _0}} $ and $z = l$ . Here, $l$ is the length of a wire, $C$ is a $CR$ capacitance and $R$ is a resistance. All other symbols have standard meanings.
A semi circular arc of radius $r$ and a straight wire along the diameter, both are carrying same current $i.$ Find out magnetic force per unit length on the small element $P$, which is at the centre of curvature.
A conducting wire bent in the form of a parabola $y^2 = 2x$ carries a current $i = 2 A$ as shown in figure. This wire is placed in a uniform magnetic field $\vec B = - 4\,\hat k$ $Tesla$. The magnetic force on the wire is (in newton)
A wire bent in the shape of a regular $n$-polygonal loop carries a steady current $I$. Let $l$ be the perpendicular distance of a given segment and $R$ be the distance of a vertex both from the centre of the loop. The magnitude of the magnetic field at the centre of the loop is given by