Heart-lung machines and artifical kidney machines employ blood pumps. A mechanical pump can mangle blood cells.Figure represents an electromagnetic pump. The blood is confined to an electrically insulating tube, represented as a rectangle of width $\omega$ and height $h.$ Two electrodes fit into the top and the bottom of the tube. The potential difference between them establishes an electric current through the blood, with current density $J$ over a section of length $L.$ A perpendicular magnetic field exists in the same region. The section of liquid in the magnetic field experiences a pressure increase given by :-
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A particle of specific charge (charge/mass) $\alpha$ starts moving from the origin under the action of an electric field $\vec E = {E_0}\hat i$ and magnetic field $\vec B = {B_0}\hat k$. Its velocity at $(x_0 , y_0 , 0)$ is ($(4\hat i + 3\hat j)$ . The value of $x_0$ is:
A long solenoid of $50\, cm$ length having $100$ turns carries a current of $2.5$ $A.$ The magnetic field at the centre of the solenold is $...... \times 10^{-5}\;T$
$\left(\mu_{0}=4 \pi \times 10^{-7}\, T\, m\, A ^{-1}\right)$
A circular conducting loop of radius $R$ carries a current $I.$ Another straight infinite conductor carrying current $I$ passes through the diameter of this loop as shown in the figure. The magnitude of force exerted by the straight conductor on the loop is
A moving coil galvanometer of resistance $100 \,\Omega$ is used as an ammeter using a resistance $0.1 \,\Omega$. The maximum deflection current in the galvanometer is $100\,\mu A$. Find the minimum current in the circuit so that the ammeter shows maximum deflection ............... $mA$
Two charged particles of mass $m$ and charge $q$ each are projected from origin simultaneously with same speed $V$ in transverse magnetic field. If ${\vec r_1}$ and ${\vec r_2}$ are the position vectors of particles (with respect to origin) at $t = \frac{{\pi m}}{{qB}}$ then the value of ${\vec r_1}.{\vec r_2}$ at that time is
A square loop of side $l$ is kept in a uniform magnetic field $B$ such that its plane makes an angle $\alpha$ with $\vec{B}$. The loop carries a current $i$. The torque experienced by the loop in this position is
A square loop of edge length $2 \mathrm{~m}$ carrying current of $2 \mathrm{~A}$ is placed with its edges parallel to the $\mathrm{x}-\mathrm{y}$ axis. A magnetic field is passing through the $x-y$ plane and expressed as $\vec{B}=B_0(1+4 x) \hat{k}$, where $\mathrm{B}_0=5 \mathrm{~T}$. The net magnetic force experienced by the loop is. . . . . . . $\mathrm{N}$.
A steady current $I$ goes through a wire loop $\mathrm{PQR}$ having shape of a right angle triangle with $\mathrm{PQ}=3 x, \mathrm{PR}=4 x$ and $\mathrm{QR}=5 x$. If the magnitude of the magnetic field at $\mathrm{P}$ due to this loop is $k\left(\frac{\mu_0 I}{48 \pi x}\right)$, find the value of $k$.
A power line lies along the east-west direction and carries a current of $10\, ampere$. The force per metre due to the earth's magnetic field of ${10^{ - 4}}\,tesla$ is