A particle of mass 1 × 10 - 26 kg and charge + 1 . 6 × 10 - 19 C travelling with a velocity 1.28 × 10 6 ms − 1 in the + x direction enters a region in which a uniform electric field E and a uniform magnetic field of induction B are present such that E x = E y = 0 , E z = − 102.4 kV m − 1 and B x = B z = 0 , B y = 8 × 10 − 2 weber / m 2 . The particle enters this region at the origin at time t = 0 . Determine the location ( x , y and z coordinates) of the particle at t = 5 × 10 − 6 s . If the electric field is switched off at this instant (with the magnetic field still present), what will be the position of the particle at t = 7.45 × 10 − 6 s ?

m = 1 × 10 − 26 kg q = 1.6 × 10 − 19 C v = 1.28 × 10 6 ms − 1 E z = − 102.4 k V m B y = 8 × 10 − 2 wb m − 2 Force by electric field F → E = q E → = 1.6 × 10 − 19 × 102.4 × 10 3 − k ^ N F → E = 163 . 84 × 10 - 16 ( - k ^ ) N Force by magnetic field = F m = q v → × B → = 1.6 × 10 − 19 [ ( 1.28 × 10 6 i ^ ) × ( 8 × 10 − 2 j ^ ) ] N = 1.6 × 10 − 19 × 102.4 × 10 3 k ^ N F → m = 163 . 84 × 10 - 16 ( k ^ ) N F → E = − F → M Till t = 6 × 10 − 6 sec So till t = 5 × 10 - 6 sec it moves without deflection So x coordinate = v t = 1.28 × 10 6 × 5 × 10 − 6 = 6.4 m So coordinate x , y , z = 6.4 m , 0 , 0 After 5 × 10 - 6 sec E → is switched off, so force on the particle is due to magnetic field which is towards + z axis. Due to this force particle starts moving in circular path in x-z plane and its time period is; T = 2 π m q B = 2 × 3.14 × 10 − 26 1.6 × 10 − 19 × 8 × 10 − 2 = 4.90 × 10 − 6 sec Radius of this circular path is; r = m v q B = 1 × 10 − 26 × 1.28 × 10 6 1.6 × 10 − 19 × 8 × 10 − 2 = 1 m Now, t 2 = 7.45 × 10 − 6 sec t 2 − t 1 = 2.45 × 10 − 6 sec So t 2 − t 1 = T 2 So particle cover 2 r distance in + z direction in circle So z -coordinate = 2 r = 2 m So coordinates x , y , z = 6.4 m , 0 , 2 m

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A non-uniform magnetic field $\vec{B} = B_{0} (1 + \frac{y}{d}) \hat{k}$ is present in region of space in between $y = 0$ and $y = d$ . The lines are shown in the diagram. A particle of mass ' $m$ ' and positive charge ' $q$ ' is moving. Given an initial velocity $\vec{v} = v_{0} \hat{i}$ . Find the component of velocity of the particle when leaves the field.

Important Questions on Magnetic Effect of Current

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Beta Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise-4>Q 11

A very long straight conductor has a circular cross-section of radius $R$ and carries a current density $J$ . Inside the conductor there is a cylindrical hole of radius a whose axis is parallel to the axis of the conductor and a distance $b$ from it. Let the $z$ -axis be the axis of the conductor, and let axis of the hole be at $x = b$ . Find the magnetic field (i) on the $x$ -axis at $x = 2 R$ (ii) on the $y$ -axis at $y = 2 R$

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Beta Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise-4>Q 12

A particle of mass

1 \times 10^{- 26} kg

and charge

+ 1.6 \times 10^{- 19} C

travelling with a velocity

1.28 \times 10^{6} {ms}^{- 1}

in the

+ x

direction enters a region in which a uniform electric field

E

and a uniform magnetic field of induction

B

are present such that

E_{x} = E_{y} = 0, E_{z} = - 102.4 kV m^{- 1}

and

B_{x} = B_{z} = 0, B_{y} = 8 \times 10^{- 2} weber / m^{2}

. The particle enters this region at the origin at time

t = 0

. Determine the location (

\Rightarrow v_{x} = v_{0} - \frac{3}{2} (\frac{q B_{0} d}{m})

and

z

coordinates) of the particle at

t = 5 \times 10^{- 6} s

. If the electric field is switched off at this instant (with the magnetic field still present), what will be the position of the particle at

t = 7.45 \times 10^{- 6} s

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Beta Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise-4>Q 13

A wire loop carrying current $I$ is placed in the $X - Y$ plane as shown in the figure (i) If a particle with charge $+ Q$ and mass $m$ is placed at the centre $P$ and given a velocity along $N P$ (figure). Find its instantaneous acceleration. (ii) $I$ an external uniform magnetic induction field $\vec{B} = B \hat{i}$ is applied, find the torque acting on the loop due to the field.

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Beta Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise-4>Q 14

Find the work and power required to move the conductor of length $l$ shown in the figure one full turn in the anticlockwise direction at a rotational frequency of $n$ revolutions per second if the magnetic field is of magnitude $B_{0}$ every where and points radially outwards from $Z$ -axis. The figure shows the surface traced by the wire $A B$ .

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Beta Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise-4>Q 15

The figure shows a conductor of weight $1.0 N$ and length $L = 0.5 m$ placed on a rough inclined plane making an angle $30$ with the horizontal so that conductor is perpendicular to a uniform horizontal magnetic field of induction $B = 0.10 T$ . The coefficient of static friction between the conductor and the plane is $0.1$ . A current of $I = 10$ A flows through the conductor inside the plane of this paper as shown. What is the force needed to be the applied parallel to the inclined plane to sustaining the conductor at rest?

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Beta Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise-4>Q 16

An electron gun $G$ emits electron of energy $2 k e v$ travelling in the $+ v e$ $x$ -direction. The electron are required to hit the spot $S$ where $G S = 0.1 m$ & the line $G S$ makes an angle of $60 °$ with the $x$ -axis, as shown in the figure. A uniform magnetic field $\vec{B}$ parallel to $G S$ exists in the region outsides to electron gun. Find the minimum value of $B$ needed to make the electron hit at $S$ .

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Beta Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise-4>Q 18

Two concentric circular coils X and Y of radii

16 cm

and

10 cm

, respectively, lie in the same vertical plane containing the north to south direction. Coil X has

20

turns and carries a current of

16 A

; coil Y has

25 turns

and carries a current of

18 A

. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

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Beta Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise-4>Q 19

Two long straight parallel wires are $2 m$ apart, perpendicular to the plane of the paper. The wire $A$ carries a current of $9.6 A$ , directed into the plane of the paper. The wire $B$ carries a current such that the magnetic field of induction at the point $P$ , at a distance of $\frac{10}{11} m$ from the wire $B$ , is zero. Find

(i) The magnitude and direction of the current in $B$ .

(ii) The magnitude of the magnetic field due to induction at the point $S$ .

(iii) The force per unit length on the wire $B$ .

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A non-uniform magnetic field B→=B01+ydk^ is present in region of space in between y=0 and y=d. The lines are shown in the diagram. A particle of mass 'm' and positive charge 'q' is moving. Given an initial velocity v→=v0i^. Find the component of velocity of the particle when leaves the field.

Important Questions on Magnetic Effect of Current

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