The magnetic field at the origin due to a current element \(i\vec{dl}\) placed at a position \(\vec r\) is
(a). \(\frac{\mu_{0} i_{}{}}{4 \pi} \frac{d\vec{l} \times \vec{r}}{r^{3}}\)
(b). \(-\frac{\mu_{0} i_{}{}}{4 \pi} \frac{\vec{r} \times d\vec{l}}{r^{3}}\)
(c). \(\frac{\mu_{0} i_{}{}}{4 \pi} \frac{\vec{r} \times d\vec{l}}{r^{3}}\)
(d). \(-\frac{\mu_{0} i_{}{}}{4 \pi} \frac{d\vec{l} \times \vec{r}}{r^{3}}\)

Choose the correct option: 
1. (a), (b)
2. (b), (c)
3. (c), (d)
4. (a), (d)

Consider three quantities x = E/B, y = \(\sqrt{1 / \mu_{0} \varepsilon_{0}}\) and z =  \(l \over CR\). Here, l is the length of a wire, C is a capacitance and R is resistance. All other symbols have standard meanings. 

(a) x, y have the same dimensions. 

(b) y, z have the same dimensions. 

(c) z, x have the same dimensions. 

(d) None of the three pairs have the same dimensions. 

Choose the correct option 

1. (a), (b), (c)

2. (b), (c)

3. (c), (d), (b)

4. (a), (d), (c)

A long, straight wire carries a current along the z-axis. One can find two points in the X-Y plane such that:

Choose the correct option :

A long, straight wire of radius R carries a current distributed uniformly over its cross-section. The 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. 

Choose the correct option 

1. (a), (b)

2. (b), (c)

3. (c), (d)

4. (a), (d)

A hollow tube is carrying an electric current along its length distributed uniformly over its surface. The magnetic field, 

In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero 

(a) outside the cable
(b) inside the inner conductor
(c) inside the outer conductor
(d) in between the two conductors

Choose the correct option 

1. (a) only

2. (b), (c)

3. (c), (d)

4. (a), (d)

A steady electric current is flowing through a cylindrical conductor. 

(a) The electric field at the axis of the conductor is zero.
(b) The magnetic field at the axis of the conductor is zero.
(c) The electric field in the vicinity of the conductor is zero.
(d) The magnetic field in the vicinity of the conductor is zero

Choose the correct option 

1. (a), (b)

2. (b), (c)

3. (c), (d)

4. (a), (d)

If the current is doubled, the deflection is also doubled in 

1.   a tangent galvanometer 

2.   a moving-coil galvanometer 

3.   both

4.   none. 

A very long bar magnet is placed with its north pole coinciding with the centre of a circular loop carrying an electric current i. The magnetic field due to the magnet at a point on the periphery of the wire is B. The radius of the loop is a. The force on the wire is 

1.  very nearly 2πaiB perpendicular to the plane of the wire 

2.  2πaiB in the plane of the wire 

3.  πaiB along the magnet

4.  zero.

Pick the correct options.

(a) All electrons have magnetic moment
(b) All protons have magnetic moment
(c) All nuclei have magnetic moment
(d) All atoms have magnetic moment

Choose the correct option

1. (a), (b)

2. (b), (c)

3. (c), (d)

4. (a), (d)