English
Karnataka Board PUCPUC Science Class 11

Consider a Long, Straight Wire of Cross-sectional Area a Carrying a Current I. Let There Be N Free Electrons per Unit Volume.

Advertisements
Advertisements

Question

Consider a long, straight wire of cross-sectional area A carrying a current i. Let there be n free electrons per unit volume. An observer places himself on a trolley moving in the direction opposite to the current with a speed  \[v = \frac{i}{\text{nAe}}\] and separation from the wire by a distance r. The magnetic field seen by the observer is very nearly  

Options

  • \[\frac{\mu_0 i}{2\pi r}\]
  • zero

  • \[\frac{\mu_0 i}{\pi r}\]
  • \[\frac{2 \mu_0 i}{\pi r}\]
MCQ
Advertisements

Solution

Magnetic field will be independent of the motion of the observer because the velocity with which the observer is moving is comparable to drift velocity of electron which is very small as compared to the speed of flow of current from one end of wire to other end. So it can be neglected  and hence, magnetic field due to the wire w.r.t the observer will be

B = \[\frac{\mu_o i}{2\pi r}\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 35: Magnetic Field due to a Current - MCQ [Page 249]

APPEARS IN

HC Verma Concepts of Physics Volume 1 and 2 [English]
Chapter 35 Magnetic Field due to a Current
MCQ | Q 12 | Page 249

RELATED QUESTIONS

Two identical coils P and Q each of radius R are lying in perpendicular planes such that they have a common centre. Find the magnitude and direction of the magnetic field at the common centre of the two coils, if they carry currents equal to I and \[\sqrt{3}\] I respectively.


A point charge q moving with speed v enters a uniform magnetic field B that is acting into the plane of the paper as shown. What is the path followed by the charge q and in which plane does it move?


 If an electric field \[\vec{E}\] is also applied such that the particle continues moving along the original straight line path, what should be the magnitude and direction of the electric field \[\vec{E}\] ?


Two long straight parallel conductors carrying steady currents I1 and I2 are separated by a distance 'd'. Explain briefly, with the help of a suitable diagram, how the magnetic field due to one conductor acts on the other. Hence deduce the expression for the force acting between the two conductors. Mention the nature of this force.


Two proton beams going in the same direction repel each other whereas two wires carrying currents in the same direction attract each other. Explain.


A moving charge produces


Consider the situation shown in figure. The wire PQ has mass m, resistance r and can slide on the smooth, horizontal parallel rails separated by a distance l. The resistance of the rails is negligible. A uniform magnetic field B exists in the rectangular region and a resistance R connects the rails outside the field region. At t = 0, the wire PQ is pushed towards right with a speed v0. Find (a) the current in the loop at an instant when the speed of the wire PQ is v, (b) the acceleration of the wire at this instant, (c) the velocity vas a functions of x and (d) the maximum distance the wire will move.


Consider the situation shown in figure. The wires P1Q1 and P2Q2 are made to slide on the rails with the same speed 5 cm s−1. Suppose the 19 Ω resistor is disconnected. Find the current through P2Q2 if (a) both the wires move towards right and (b) if P1Q1 moves towards left but P2Q2 moves towards right.


The current generator Ig' shown in figure, sends a constant current i through the circuit. The wire ab has a length l and mass m and can slide on the smooth, horizontal rails connected to Ig. The entire system lies in a vertical magnetic field B. Find the velocity of the wire as a function of time.


An electron having a charge e moves with a velocity v in X-direction. An electric field acts on it in Y-direction? The force on the electron acts in ______.

A beam of protons with speed 4 × 105 ms-1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to :

(Mass of the proton = 1.67 × 10-27 kg, charge of the proton = 1.69 × 10-19 C)


A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 × 10-5 T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in µV) in the coil will be close to the integer ______.


A thin strip 10 cm long is on a U-shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm-1. The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance is 10 Ω, and air drag is negligible, N will be close to ______.


A wire carrying current i has the configuration shown in figure. For the magnetic field to be zero at the centre of the circle, θ must be:


Protons and singly ionized atoms of U235 and U238 are passed in turn (which means one after the other and not at the same time) through a velocity selector and then enter a uniform magnetic field. The protons describe semicircles of radius 10 mm. The separation between the ions of U235 and U238 after describing the semicircle is given by ______.


A charged particle of charge q and mass m is projected in a region that contains an electric and magnetic field as shown in the figure with velocity V at an angle of 45° with x-direction. If V = `sqrt((qE)/m)`, then net deviation in particle motion will be (neglect the effect of gravity) in a clockwise direction approx ______ °.

 


An electron (mass 9 × 10−31 kg and charge 1.6 × 10−19 C) moving with speed c/100 (c = speed of light)is injected into a magnetic field `vecB` of magnitude 9 × 104 T perpendicular to its direction of motion. We wish to apply an uniform electric field `vecE` together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3 × 108 m s−1).


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×