Magnetic Field Due to Straight Current Carrying Wire

Practice Questions:

Question 1: difficult

A long straight wire along the z-axis carries a current I in the negative z-direction. The magnetic
vector field \[\overrightarrow{B}\] at a point having coordinates (x, y) in the z = 0 plane is :

1. \[\frac{\mu_{0}I}{2\pi}\left( \frac{y\hat{i}-x\hat{j}}{x^{2}+y^{2}} \right)\]

2. \[\frac{\mu_{0}I}{2\pi}\left( \frac{x\hat{i}+y\hat{j}}{x^{2}+y^{2}} \right)\]

3. \[\frac{\mu_{0}I}{2\pi}\left( \frac{x\hat{j}-y\hat{i}}{x^{2}+y^{2}} \right)\]

4. \[\frac{\mu_{0}I}{2\pi}\left( \frac{x\hat{i}-y\hat{j}}{x^{2}+y^{2}} \right)\]

View Answer

💬 Discuss this Question

Question 2: difficult

A long wire carrying a current of 2 A is laid along the x axis (current flows along positive
x direction) and another wire carrying current of 4 A is laid along y axis(current flows along
positive y direction). The points at which magnetic field is zero are:

1. (2, 1, 0)

2. (1, 2, 0)

3. (6, 3, 1)

4. (–2, 4, 0)

View Answer

💬 Discuss this Question

Question 3: difficult

A cube made of wires of equal length is connected to a battery as shown in the figure. The magnetic field at the centre of the cube is :

1. \[\frac{12\mu_{0}I}{\sqrt{2}\pi L}\]

2. \[\frac{6\mu_{0}I}{\sqrt{2}\pi L}\]

3. \[\frac{6\mu_{0}I}{\pi L}\]

4. zero

View Answer

💬 Discuss this Question

Question 4: difficult

Adjoining figure shows a rectangular loop of conductor carrying a current i. The length and breadth of the loop are respectively a and b. The magnetic field at the centre of loop is :

1. \[\frac{\mu_{0}i\left( a+b \right)}{2\pi \sqrt{a^{2}+b^{2}}}\]

2. \[\frac{\mu_{0}iab}{2\pi \sqrt{a^{2}+b^{2}}}\]

3. \[\frac{\mu_{0}i\left( a+b \right)}{\pi \sqrt{a^{2}+b^{2}}}\]

4. \[\frac{2\mu_{0}i\sqrt{a^{2}+b^{2}}}{\pi ab}\]

View Answer

💬 Discuss this Question

Question 5: difficult

Two long parallel wires are at a distance 2d apart. The carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX’ is given by :

View Answer

💬 Discuss this Question

Question 6: difficult

Two identical wires A and B have the same length l and carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side a. If B1 and B2 are the values of magnetic induction at the centre of the circle and the centre of the square, respectively. then the ratio B1/B2 is :

1. (π² / 8)

2. (π² / 8√2)

3. (π² / 16)

4. (π² / 16√2)

View Answer

💬 Discuss this Question

Question 7: difficult

The magnetic field at center O of the arc in figure is :

1. \[\frac{\mu_{0}I}{4\pi\times r}\left[ \sqrt{2} +\pi \right]\]

2. \[\frac{\mu I}{2\pi r}\left[\frac{\pi}{4}+ \left( \sqrt{2}- 1 \right)\right]\]

3. \[\frac{\mu_{0}}{2\pi }\times \frac{I}{r}[\sqrt{2}-\pi ]\]

4. \[\frac{\mu_{0}}{4\pi }\times \frac{I}{r}[\sqrt{2}+\frac{\pi}{4} ]\]

View Answer

💬 Discuss this Question

Question 8: difficult

A straight section PQ of a circuit lies along the X-axis form x = –a/2 to x = a/2 and carries a steady current i. The magnetic field due to the section PQ at a point X = +a will be :

1. Proportional to a

2. Proportional to a²

3. Proportional to 1/a

4. Zero

View Answer

💬 Discuss this Question

Question 9: difficult

A long straight wire carrying a current of 30A is placed in an external uniform magnetic field
of induction \[4\times 10^{-4} T\]. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point 2.0 cm away from the wire is
\[\left( \mu_{0}=4\pi\times 10^{-7}H/m \right)\]:

1. \[10^{-4}\]

2. \[3\times 10^{-4}\]

3. \[5\times 10^{-4}\]

4. \[6\times 10^{-4}\]

View Answer

💬 Discuss this Question

Question 10: difficult

What will be the resultant magnetic field at origin due to four infinite length wires. If each wire produces magnetic field ‘B’ at origin: