Magnetic Field Due to a Straight Long Wire

Q. A uniform electric field $E$ is created between two parallel and oppositely charged plates as shown in figure. An electron enters the field symmetrically between the plates with a speed $v_0$. The length of each plate is $l$. Find the angle of deviation (which is given by $\theta$ in the figure) of the path of the electron as it comes out of the field interms of mass of electron $m$ and charge of the electron $e$. (Acceleration due to gravity can be neglected)

1. $\theta ={\tan }^{-1}\left(\frac{2eEl}{m{v}_0^2}\right)$
2. $\theta ={\tan }^{-1}\left(\frac{eEl}{m{v}_0^2}\right)$
3. $\theta ={\cot }^{-1}\left(\frac{2eEl}{m{v}_0^2}\right)$
4. $\theta ={\tan }^{-1}\left(\frac{eE}{m{v}_0^2}\right)$

Q. Two infinitely long insulated wires are kept perpendicular to each other. They carry currents $I_1=2A$ and $I_2=1.5A$.
i) Find the magnitude and direction of the magnetic field at P.
ii) If the direction of current is reversed in one of the wires. What would be the magnitude of the field B?

1. $2\times {10}^{-5}T$, normally into the plane of the paper, $2\sqrt{2}\times {10}^{-5}T$
2. $2\times {10}^{-5}T$, normally out of the plane of the paper, $2\sqrt{2}\times {10}^{-5}T$
3. $2\times {10}^{-5}T$, normally into the plane of the paper, Zero
4. $2\times {10}^{-5}T$, normally into the plane of the paper, Zero

Q.

An electric current is flowing in a long straight wire. The magnetic field due to this current a distance of 5 cm from the wire is 10 T. The magnetic field at a distance of 10 cm from the wire is

1. 2.5 T

2. 5 T

3. 20 T

4. 40 T

Q.

A wire ABCDEF (with each side of length L) bent as shown in Fig. and carrying a current I is placed in a uniform magnetic field B parallel to the positive y - direction. What is the magnitude and direction of the force experienced by the wire?

1. BIL along positive z-direction

2. $\frac{B{I}^2}{L}$ along positive z-direction

3. BIL along negative z-direction

4. $\frac{BL}{I}$ along negative z-direction

Q.

The strength of the magnetic field at a point r near a long straight current carrying wire is B. The field at a distance $\frac{r}{2}$ will be

[MP PMT 1990]

1. $\frac{B}{2}$

2. $\frac{B}{4}$

3. 2B

4. 4B

Q. Find the magnetic field due to a square frame of side a carrying a current as shown at 0.

1. $Zero$
2. $\frac{\left(2{\mu }_{0}i\right)}{\pi a}$
3. $\frac{{\mu }_{0}i}{2\sqrt{2}\pi a}$
4. $2\frac{\sqrt{2}{\mu }_{0}i}{\pi a}$

Q. Formula for calculating magnetic field due to infinite wire can be derived from the formula of magnetic field due to finite wire.

1. False
2. True

Q.

Two straight and long conductors AOB and COD are perpendicular to each other and carry currents of $I_{1}and{I}_2$. The magnitude of the magnetic field at a point P at a distance a from point 0 in a direction perpendicular to the plane ABCD is

1. $\frac{{\mu }_0}{2\pi a}(I_1+I_2)$

2. $\frac{{\mu }_0}{2\pi a}(I_1-I_2)$

3. $\frac{{\mu }_0}{2\pi a}(I_1^2+I_2^2{)}^{\frac{1}{2}}$

4. $\frac{{\mu }_0}{2\pi a}\frac{I_1{I}_2}{(I_1+I_2)}$

Q. A long vertical wire carrying a current of 1A in the upward direction is placed in a region where a horizontal magnetic field of $2.0\times {10}^{-4}T$ exists from south to north. Find the point where the resultant magnetic field is zero.

1. 1.0mm, to the west of the wire
2. 1.0 mm, to the East of the wire
3. 2.0 mmm to the North of the wire
4. 2.0 mm, to the South of the wire

Q. An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR The magnetic field due to this current at the point M is $H_1$. Now another infinitely long straight conductor QS is connected at Q so that the current is I/2 in QR as well as in QS, The current in PQ remaining unchanged. The magnetic field at M is now $H_2$ The ratio $\frac{H_1}{H_2}$ is given by

1. $\frac{1}{2}$
2. $1$
3. $\frac{2}{3}$
4. $2$

Q.

A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the sides of the loop. If a steady current I is established in the wire, as shown in Fig., the loop

1. rotate about an axis parallel to the wire

2. move away from the wire

3. move towards the wire

4. remain stationary.

Q. If a copper rod carries a direct current, the magnetic field associated with the current will be

1. Only inside the rod
2. Only outside the rod
3. Both inside and outside the rod
4. Neither inside nor outside the rod

Q.

The magnetic induction at a point P which is distant 4 cm from a long current carrying wire is ${10}^{-3}$ Telsa.The field of induction at a distance 12 cm from the same current would be

1. $3.33\times {10}^{-9}$ Tesla

2. $1.11\times {10}^{-4}$ Tesla

3. $3\times {10}^{-3}$ Tesla

4. $9\times {10}^{-2}$ Tesla

Q.

Three infinitely long wires are arranged at the virtices of an equilateral triangle of side a. Find $B_0$

1. $Zero$

2. $\frac{{\mu }_{0}i}{\sqrt{3}\pi a}$

3. $\frac{{\mu }_{0}i}{2\pi R}$

4. $\frac{\sqrt{2}{\mu }_{0}i}{3\pi R}$