An electron, moving in a uniform magnetic field of induction of intensity $\stackrel{\rightharpoonup }{B,}$ has its radius directly proportional to :

(1) Its charge                       

(2) Magnetic field

(3) Speed                               

(4) None of these

What is a representation of the magnetic field caused by a straight conductor with a uniform cross-section and a steady current of radius 'a'?

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3.		4.

A non-planar loop of conducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic field due to this loop at the point P (a,0,a) points in the direction

(1)  $\frac{1}{\sqrt{2}}\left(-\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$                                   

(2) $\frac{1}{\sqrt{3}}(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$

(3)  $\frac{1}{\sqrt{3}}(-\hat{\mathrm{j}}+\hat{\mathrm{k}}+\hat{\mathrm{i}})$                             

(4)  $\frac{1}{\sqrt{2}}(\hat{\mathrm{i}}+\hat{\mathrm{k}})$                        

A particle of charge q and mass m is moving along the x-axis with a velocity of v and enters a region of electric field E and magnetic field B as shown in the figure below. For which figure is the net force on the charge zero?

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3.		4.

A current-carrying wire is placed in a uniform magnetic field in the shape of the curve \(y= \alpha sin ({\pi x \over L}),~0 \underline{<}x \underline{<}~2L\) $$
. What will be the force acting on the wire?
                   

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

1. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{y}\hat{\mathrm{i}}-\mathrm{x}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$                 

2. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{i}}+\mathrm{y}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{j}}-\mathrm{y}\hat{\mathrm{i}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$                 

4. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{i}}-\mathrm{y}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$

A circular coil is in the y-z plane with its centre at the origin. The coil carries a constant current. Assuming the direction of the magnetic field at x = – 25 cm to be positive, which of the following graphs shows the variation of the magnetic field along the x-axis?

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3.		4.

The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

(a) $\frac{{\mathrm{\pi }}^2}{4\sqrt{2}}$                             (b) $\frac{{\mathrm{\pi }}^2}{8\sqrt{2}}$

(c) $\frac{\mathrm{\pi }}{2\sqrt{2}}$                             (d) $\frac{\mathrm{\pi }}{4\sqrt{2}}$ 

A particle of charge +q and mass m moving under the influence of a uniform electric field $\mathrm{E}\hat{\mathrm{i}}$ and a uniform magnetic field  $\mathrm{B}\hat{\mathrm{k}}$ follows a trajectory from P to Q as shown in the figure. The velocities at P and Q are $\mathrm{v}\hat{\mathrm{i}}$ and $-2\mathrm{v}\hat{\mathrm{j}}$ respectively. Which of the following statement(s) is/are correct?

Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r

and that of ADC is 2r. The value of magnetic field at the centre of the loop assuming

uniform wire is

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

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

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

4. $\frac{\sqrt{2}{\mu }_{0}i}{\mathrm{\pi a}}\otimes$