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
Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current.
How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.
What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30° with the direction of a uniform magnetic field of 0.15 T?
Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
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.
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"`
A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section. (a) At what points will the resultant magnetic field have maximum magnitude? What will be the maximum magnitude? (b) What will be the minimum magnitude of the resultant magnetic field?
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.
Figure shows a metallic wire of resistance 0.20 Ω sliding on a horizontal, U-shaped metallic rail. The separation between the parallel arms is 20 cm. An electric current of 2.0 µA passes through the wire when it is slid at a rate of 20 cm s−1. If the horizontal component of the earth's magnetic field is 3.0 × 10−5 T, calculate the dip at the place.
Figure shows two parallel wires separated by a distance of 4.0 cm and carrying equal currents of 10 A along opposite directions. Find the magnitude of the magnetic field B at the points A1, A2, A3.
Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current by placed so that it experiences no magnetic force?
Answer the following question.
Two infinitely long straight wire A1 and A2 carrying currents I and 2I flowing in the same direction are kept' distance apart. Where should a third straight wire A3 carrying current 1.5 I be placed between A1 and A2 so that it experiences no net force due to A1 and A2? Does the net force acting on A3 depend on the current flowing through it?
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 ______.
Five long wires A, B, C, D and E, each carrying current I are arranged to form edges of a pentagonal prism as shown in figure. Each carries current out of the plane of paper.
- What will be magnetic induction at a point on the axis O? AxisE is at a distance R from each wire.
- What will be the field if current in one of the wires (say A) is switched off?
- What if current in one of the wire (say) A is reversed?
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 straight parallel current-carrying conductors are kept ‘a’ distant apart in the air. The direction of current in both the conductors is the same. Find the magnitude of force per unit length and the direction of the force between them. Hence define one ampere.
Two long, straight, parallel conductors carry currents flowing in opposite directions (antiparallel currents). The magnetic force between them is:
If the perpendicular distance d between two parallel current-carrying conductors is doubled, the force per unit length F/L:
