Magnetic Field Due to Finite Wire

Q. A closed circuit is in the form of a regular hexagon of side a. If the circuit carries current I, What is magnetic induction at the cetre of the hexagon?

1. $\frac{\sqrt{3}{\mu }_{0}i}{\pi a}$
2. $\frac{\sqrt{3}{\mu }_{0}i}{\pi a}$
3. zero
4. None

Q. A wire carrying current $i$ has the configuration as shown in the figure. Two semi-infinite straight sections, each tangent to the same circle, are connected by a circular arc, of angle $\theta ,$ along the circumference of the circle, with all sections lying in the same plane. What must $\theta (\text{in rad) be in order for}B$ to be zero at the center of circle is

Q. Find the magnetic field due to a current carrying wire at point P. (a =7 cm)

1. $2\times {10}^{-7}$ Tesla
2. $3\times {10}^{-7}$ Tesla
3. ${10}^{-5}$ Tesla
4. $7\times {10}^{-5}$ Tesla

Q. A point charge of magnitude q = 4.5 nC is moving with speed v = $3.6\times {10}^7$ m/s parallel to the x-axis along the line y = 3 m. Find the magnetic field at the origin produced by this charge when the charge is at the point x = -4 m, y = 3 m, as shown in the figure.

1. $-3.89\times {10}^{-10}\hat{k}T$
2. $3.89\times {10}^{-10}\hat{k}T$
3. $3.89\times {10}^{-10}\hat{i}T$
4. $3.89\times {10}^{-10}\hat{j}T$

Q. Magnetic field at a point r near a long straight current carrying wire is B.The field at a distance r/2

1. will be B/2
2. will be B/4
3. will be 2B
4. will be 4B

Q. A current i is flowing in a straight conductor of length L. The magnetic field at a point distant $\frac{L}{4}$ from its centre will be

1. $\frac{4{\mu }_{0}i}{\sqrt{5}\pi L}$
   
2. $\frac{4{\mu }_{0}i}{2\pi L}$
   
3. $\frac{{\mu }_{0}i}{\sqrt{2}L}$
4. $Zero$