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Question no. 6

Direction of propagation of electromagnetic wave is determined from its phase term .

For the given electromagnetic wave , phase term is " k z - ω t " .

Hence , given electromagnetic wave is propagating in z-axis direction , or in the direction of unit vector k .

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Question no. 7

Velocity of charged particle has components along x-axis and z-axis.

Since the magnetic field is along z-axis , component along x-axis gives magnetic force that makes the charged particle to move in circular motion.

velocity component along z-axis moves the charged particle along z-axis.

Hence , overall effect is helical path for the charged particle and the charged particle makes displacement along z-axis.

Time taken by the charged particle to move 2 m above x-y plane , i.e., along z-axis is ( distance / speed ) = ( 2  / 4 ) = 1/2 sec

Hence ansere is :- (B) Helical path, 1/2 s

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Question No. 8

Figure shows the electric dipole p is palced along z-axis.

Work done to move the charge q from A ( a, 0, 0) to B (0, 0, a ) is difference of potential energy between A and B.

Electric potential V at a point due to dipole p is

where K = 1/(4πεo) is Coulomb's constant, θ is angle between the axis of dipole and the line joining dipole and the point where potential is measured.

r is the distance between dipole and the point where potential is measured.

Potential energy UA of charge q  at A is zero because angle θ = 90° and cosθ = 0 .

UA = 0

Potential energy UB of charge q at B is

Hence work done is ( UB - UA ) =  q × K × ( p / a2 )

Answered by Thiyagarajan K | 20 Apr, 2024, 09:29: AM

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