Magnetic Effects of Current

Consider the two idealised systems (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length L >> R, radius of cross – section. In (i) E is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below.

Q: Consider the two idealised systems (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length L >> R, radius of cross – section. In (i) E is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below.

(a) Case (i) contradicts gauss’ law for electrostatic fields

(b) Case (ii) contradicts Gauss’law for magnetic fields

(c) Case (i) agrees with $\oint \vec{E}.\vec{dl} = 0 $

(d) Case (ii) contradicts $\oint \vec{E}.\vec{dl} = I_{en} $

Click to See Answer :
Ans: (b)

 

The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The dipole axis makes an angle of 11.3° with axis of the earth. At Mumbai, declination is nearly zero. Then,

Q: The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The dipole axis makes an angle of 11.3° with axis of the earth. At Mumbai, declination is nearly zero. Then,

(a) The declination varies between 11.3° W to 11.3°E

(b) The least declination is 0°

(c) The plane defined by dipole axis and the earth axis passes through Greenwich

(d) Declination averaged over the earth must be always negative

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Ans: (a)

 

A toroid of n turns, mean radius R and cross – sectional radius a carries current I. It is placed on a horizontal table taken as xy – plant. Its magnetic moment m

Q: A toroid of n turns, mean radius R and cross – sectional radius a carries current I. It is placed on a horizontal table taken as xy – plant. Its magnetic moment M

(a) Is non- zero and points in the z- direction by symmetry

(b) Points along the axis of the toroid $\vec{M} = M\hat{\phi}$

(c) Is zero, otherwise there would be a field falling as 1/r3 at large distances outside the toroid

(d) Is pointing radially outwards

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Ans: (c)

 

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.

Q: 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.

Numerical

(a) What will be magnetic induction at a point on the axis 0? Axis is at a distance R from each wire.
(b) What will be the field if current in one of the wires (say A) is switched off?
(c) What if current in on of the wire (say A) is reversed?

An electron an a positron are released from (0, 0, 0) and (0, 0, 1.5R) respectively, in a uniform magnetic field B = B0i ̂, each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will be orbits be non – intersecting circles ?

Q: An electron an a positron are released from (0, 0, 0) and (0, 0, 1.5R) respectively, in a uniform magnetic field $B = B_o \hat{i}$ each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will be orbits be non – intersecting circles?