Two parallel wires carry currents of 20 A and 40 A in opposite directions. Another wire carrying a current antiparallel to 20 A is placed midway between the two wires. The magnetic force on it will be

1.   towards 20 A

2.   towards 40 A

3.   zero

4.   perpendicular to the plane of the currents

Two parallel, long wires carry currents i₁, and i₂ with i₁ > i₂. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 µT. If the direction of i₂ is reversed, the field becomes 30 µT. The ratio i₁/i₂ is

1.   4

2.   3

3.   2

4.   1

Consider a long, straight wire of cross-sectional area A carrying a current i. Let there be n free electrons per unit volume. An observer places himself on a trolley moving in the direction opposite to the current with a speed v = \(\frac{\mathrm{i}}{\mathrm{n} \mathrm{Ae}}\)and separated from the wire by a distance r. The magnetic field seen by the observer is very nearly

1.    \(\frac{\mu_{0} i}{2 \pi r}\) 

2.   Zero

3.   \(\frac{\mu_{0} i}{ \pi r}\) 

4.   \(\frac{2\mu_{0} i}{\pi r}\) 

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)