A thick current-carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by:
 

1.		2.
3.		4.

An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of ${10}^5$ m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

   

1. $4\mathrm{\pi }\times {10}^{-20} \mathrm{N}$

2. $8\times {10}^{-20} \mathrm{N}$

3. $4\times {10}^{-20} \mathrm{N}$

4. $8\mathrm{\pi }\times {10}^{-20} \mathrm{N}$

A uniform conducting wire of length \(12a\) and resistance 'R' is wound up as a current carrying coil in the shape of,

(i) an equilateral triangle of side 'a'

(ii) a square of side 'a'

The magnetic dipole moments of the coil in each case respectively are:

1. $3{\mathrm{Ia}}^2 \mathrm{and} 4{\mathrm{Ia}}^2$

2. $4{\mathrm{Ia}}^2 \mathrm{and} 3{\mathrm{Ia}}^2$

3. $\sqrt{3}{\mathrm{Ia}}^2 \mathrm{and} 3{\mathrm{Ia}}^2$

4. $3{\mathrm{Ia}}^2 \mathrm{and} {\mathrm{Ia}}^2$

In the product
\(\vec{F}=q\left ( \vec{v}\times \vec{B} \right )\\~~~=q\vec{v}\times \left ( B\hat{i}+B\hat{j}+B_0\hat{k} \right )\)
For \(q=1\) and \(\vec{v}=2\hat{i}+4\hat{j}+6\hat{k}\) 
and \(\vec{F}=4\hat{i}-20\hat{j}+12\hat{k}\)
What will be the complete expression for \(\vec{B}\)?
1. \(8\hat{i}+8\hat{j}-6\hat{k}\)
2. \(6\hat{i}+6\hat{j}-8\hat{k}\)
3. \(-8\hat{i}-8\hat{j}-6\hat{k}\)
4. \(-6\hat{i}-6\hat{j}-8\hat{k}\)

A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is:

$\left({\mathrm{\mu }}_0=4\mathrm{\pi }\times {10}^{-7} \mathrm{T} \mathrm{m} {\mathrm{A}}^{-1}\right)$

1.  $3.4\times {10}^{-4}T$

2.  $6.28\times {10}^{-5}T$

3.  $3.14\times {10}^{-5}T$

4.  $6.28\times {10}^{-4}T$

A wire of length L metres carrying a current of 1 amp is bent in the form of a circle. What is its magnetic moment?

1.  $\frac{{\mathrm{IL}}^2}{4} \mathrm{A}-{\mathrm{m}}^2$

2.  $\frac{\mathrm{I}\times {\mathrm{\pi L}}^2}{4} \mathrm{A}-{\mathrm{m}}^2$

3.  $\frac{2{\mathrm{IL}}^2}{\mathrm{\pi }} \mathrm{A}-{\mathrm{m}}^2$

4.  $\frac{{\mathrm{IL}}^2}{4\mathrm{\pi }} \mathrm{A}-{\mathrm{m}}^2$

A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor is correctly represented by the figure:

1.		2.
3.		4.

Ionized hydrogen atoms and α-particles with the same momenta enter perpendicular to a constant magnetic field,B. The ratio of their path radii r_H:r_α will be:

1. 1 : 4

2. 2 : 1

3. 1 : 2

4. 4 : 1

Two toroids 1 and 2 have total no. of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry the same current i, what will be the ratio of the magnetic fields along the two loops?

1. 1:1

2. 4:1

3. 2:1

4. 1:2

A straight conductor carrying current I splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is,

1.  zero

2. $\frac{3{\mu }_{0}i}{32R}, inward$

3. $\frac{3{\mu }_{0}i}{32R}, outward$

4. $\frac{{\mu }_{0}i}{2R}, inward$