Advertisements
Advertisements
Question
and ```vecE` and `vecB`denote electric and magnetic fields in a frame S and `vecE`→ and `vecB` in another frame S' moving with respect to S at a velocity `vecV` Two of the following equations are wrong. Identify them.
(a) `B_y^, = B_y + (vE_z)/c^2`
(b) `E_y^' = E_y - (vB_z)/(c^2)`
`(c) Ey = By + vE_z`
`(d) E_y = E_y + vB_z`
Advertisements
Solution
(b) `E_y^' = E_y - (vB_z)/(c^2)`
`(c) Ey = By + vE_z`
Electric force due to a charged particle is q E and magnetic force is q V B.
We can sort out the two wrong equations using dimensional analysis. Now, equating the above two forces. we get:
E = V B
Hence, analysing the answers using dimensional analysis, we see that the second term on the RHS of the equations (b) and (c) are not dimensionally correct. Thus, the options (b) and (c) are wrong.
APPEARS IN
RELATED QUESTIONS
Two infinitely long straight parallel wires, '1' and '2', carrying steady currents I1 and I2 in the same direction are separated by a distance d. Obtain the expression for the magnetic field `vecB`due to the wire '1' acting on wire '2'. Hence find out, with the help of a suitable diagram, the magnitude and direction of this force per unit length on wire '2' due to wire '1'. How does the nature of this force changes if the currents are in opposite direction? Use this expression to define the S.I. unit of current.
Two long straight parallel conductors 'a' and 'b', carrying steady currents Ia and Ib are separated by a distance d. Write the magnitude and direction of the magnetic field produced by the conductor 'a' at the points along the conductor 'b'. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors?
Two infinitely large plane thin parallel sheets having surface charge densities σ1 and σ2 (σ1 > σ2) are shown in the figure. Write the magnitudes and directions of the net fields in the regions marked II and III.
An electron beam projected along the positive x-axis deflects along the positive y-axis. If this deflection is caused by a magnetic field, what is the direction of the field? Can we conclude that the field is parallel to the z-axis?
A charged particle goes undeflected in a region containing an electric and a magnetic field. It is possible that
(a) `vecE" || "vecB , vecv" || " vec E `
(b) `vecE "is not parallel" vecB`
(c) `vecv " || " vecB but vecv "is not parallel"`
(d) `vecE" || " vecB but vecv "is not parallel"`
Two parallel, long wires carry currents i1 and i2 with i1 > i2. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 µT. If the direction of i2 is reversed, the field becomes 30 µT. The ratio i1/i2 is
A long, straight wire of radius R carries a current distributed uniformly over its cross section. T he magnitude of the magnetic field is
(a) maximum at the axis of the wire
(b) minimum at the axis of the wire
(c) maximum at the surface of the wire
(d) minimum at the surface of the wire.
A current of 10 A is established in a long wire along the positive z-axis. Find the magnetic field \[\vec{B}\] at the point (1 m, 0, 0).
A transmission wire carries a current of 100 A. What would be the magnetic field B at a point on the road if the wire is 8 m above the road?
A hypothetical magnetic field existing in a region is given by `vecB = B_0 vece` where `vece`_r denotes the unit vector along the radial direction. A circular loop of radius a, carrying a current i, is placed with its plane parallel to the x−y plane and the centre at (0, 0, d). Find the magnitude of the magnetic force acting on the loop.
A rectangular coil of 100 turns has length 5 cm and width 4 cm. It is placed with its plane parallel to a uniform magnetic field and a current of 2 A is sent through the coil. Find the magnitude of the magnetic field B if the torque acting on the coil is 0.2 N m−1
Two long, straight wires, each carrying a current of 5 A, are placed along the x- and y-axis respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points (a) (1 m, 1 m), (b) (−1 m, 1 m), (c) (−1 m, −1 m) and (d) (1 m, −1 m).
A long, straight wire carries a current i. Let B1 be the magnetic field at a point P at a distance d from the wire. Consider a section of length l of this wire such that the point P lies on a perpendicular bisector of the section B2 be the magnetic field at this point due to this second only. Find the value of d/l so that B2 differs from B1 by 1%.
A conducting circular loop of radius a is connected to two long, straight wires. The straight wires carry a current i as shown in figure. Find the magnetic field B at the centre of the loop.
If a current I is flowing in a straight wire parallel to x-axis and magnetic field is there in the y-axis then, ______.
A milli voltmeter of 25 milli volt range is to be converted into an ammeter of 25 ampere range. The value (in ohm) of necessary shunt will be ______.
Three infinitely long parallel straight current-carrying wires A, B and C are kept at equal distance from each other as shown in the figure. The wire C experiences net force F. The net force on wire C, when the current in wire A is reversed will be ______.
Two long straight parallel conductors carrying currents I1 and I2 are separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field produced by one exerts an attractive force on the other. Obtain the expression for this force and hence define 1 ampere.
Two long parallel wires kept 2 m apart carry 3A current each, in the same direction. The force per unit length on one wire due to the other is ______.
