Find force per unit length at $P$.
AIIMS 2019, Medium
Download our app for free and get startedPlay store
The magnetic field at $B$,

$B=\frac{\mu_{0} i}{4 \pi r}+0+\frac{\mu_{0} i}{4 \pi r}$

$=\frac{\mu_{0} \times 5}{4 \pi \times 5 \times 10^{-2}} \times 2$

$=\frac{\mu_{0}}{4 \pi} \times 200$

$=2 \times 10^{-5} T$

Consider the length of wire element at $P$ is $dl$.

The force per unit length at $P$ is,

$F=i B d l$

$\frac{F}{d l}=i B$

$=5 \times 2 \times 10^{-5}$

$=10^{-4} N / m$

art

Download our app
and 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

  • 1
    Assertion : A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.

    Reason : Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field $\overrightarrow B $ in a direction perpendicular to $\overrightarrow B $, will describe circular trajectories of equal radii.

    View Solution
  • 2
    A 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
  • 3
    A proton and a deutron ( $\mathrm{q}=+\mathrm{e}, m=2.0 \mathrm{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is:
    View Solution
  • 4
    The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its
    View Solution
  • 5
    A proton is accelerating in a cyclotron where the applied magnetic field is $2 \,T$. If the potential gap is effectively $100 \,kV$ then how much revolutions the proton has to make between the "dees" to acquire a kinetic energy of $20 \,MeV$ ?
    View Solution
  • 6
    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.
    View Solution
  • 7
    Two parallel long current carrying wire separated by a distance $2 \mathrm{r}$ are shown in the figure. The ratio of magnetic field at $\mathrm{A}$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is $\qquad$
    View Solution
  • 8
    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
    View Solution
  • 9
    Assertion : The magnetic field at the centre of the circular coil in the following figure due to the currents $I_1$ and $I_2$ is zero.

    Reason : $I_1 = I_2$ implies that the fields due to the current $I_1$ and $I_2$ will be balanced.

    View Solution
  • 10
    A straight wire of length $({\pi ^2})$ $metre$ is carrying a current of $2\,A$ and the magnetic field due to it is measured at a point distant $1\, cm$ from it. If the wire is to be bent into a circle and is to carry the same current as before, the ratio of the magnetic field at its centre to that obtained in the first case would be
    View Solution