An electron gun G emits electron of energy 2 keV travelling in the positive x - direction. The electrons are required to hit the spot S where GS = 0 . 1 m and the line GS makes an angle of 60 ° with the x - axis, as shown in the figure. A uniform magnetic field B parallel to GS exists in the region outside of electron gun. Find the minimum value of B needed to make the electron hit S . [Take mass of electron = 9 × 10 – 31 kg ]

The velocity V can be resolved in perpendicular and parallel direction. V cos θ component of velocity is responsible to move the charge particle in the direction of the magnetic field whereas V sin θ component is responsible for rotating the charged particle in circular motion. GS = V cos θ × T = V cos θ × 2 π m q B = 2 π q B m V cos 60 ° = π m V q B = π q B 2 m E B = π q ( GS ) 2 m E = 3 . 14 1 . 6 × 10 - 19 0 . 1 × 2 × 9 . 1 × 10 - 31 × 2 × 1 . 6 × 10 - 19 × 10 3 B = 3 . 14 4 × 9 × 10 - 28 1 . 6 × 10 - 19 = 31 . 4 × 1 . 5 × 10 - 4 = 4 . 72 × 10 - 3 T

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A proton projected in a magnetic field of $0.04 T$ travels along a helical path of radius $5.0 cm$ (of projected circle) and pitch $20 cm$ . Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the mass of the proton $= 1.6 \times 10^{- 27} kg$ .

Important Questions on Magnetic Effect of Current

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 38

An electron gun $G$ emits electron of energy $2 keV$ travelling in the positive $x -$ direction. The electrons are required to hit the spot $S$ where $GS = 0.1 m$ and the line $GS$ makes an angle of $T = \frac{2 π m}{q B}$ with the $x -$ axis, as shown in the figure. A uniform magnetic field $B$ parallel to $GS$ exists in the region outside of electron gun. Find the minimum value of $Pitch = v_{H} \times T$ needed to make the electron hit $S$ . [Take mass of electron $= 9 \times 10^{- 31} kg$ ]

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 39

An electron beam passes through a magnetic field of

2 \times 10^{- 3} Wb m^{- 2}

and an electric field of

3.2 \times 10^{4} V m^{- 1}

, both acting simultaneously.

(\vec{E} ⊥ \vec{B} ⊥ \vec{v})

If the path of electrons remains undeflected calculate the speed of the electron. If the electric field is removed, what will be the radius of the electron path [mass of electron

= 9.1 \times 10^{- 31} kg

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 40

A conducting wire of length $l$ , lying normal to a magnetic field $B$ , moves with a velocity $v$ as shown in figure (a). Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons concentrate at one end resulting in an electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when the redistribution stops. (c) What potential difference is developed between the ends of the wire?

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 42

A particle moves in a circular path of diameter

10 cm

under the action of a magnetic field of

0.40 T

. An electric field of

200 V m^{- 1}

makes the path straight. Find the charge/mass ratio of the particle.

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 43

A proton goes undeflected in a crossed electric and magnetic field (the fields are perpendicular to each other) at a speed of

10^{5} m / s

. The velocity is perpendicular to both the fields. When the electric field is switched off, the proton moves along a circle of radius

2 cm

. Find the magnitudes of the electric and the magnetic fields. Take the mass of the proton

= 1.6 \times 10^{- 27} kg

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 44

A particle

(a)

mass

m

and charge

q

is released at rest at the origin in a region in which there are electric and magnetic fields given by,

\vec{B} = - B_{0} \hat{j}

and

\vec{E} = - E_{0} \hat{k}

. Find the speed of the particle as a function of its

Z -

coordinate.

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 45

Consider a

10 cm

long portion of a straight wire carrying a current of

10 A

placed in a magnetic field of

0.1 T

making an angle of

37 °

with the wire. What magnetic force does the wire experience ?

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 46

A current of $2 A$ enters at the corner d of a square frame $abcd$ of side $10 cm$ and leaves at the opposite corner $b$ . A magnetic field $B = 0.1 T$ exists in the space in direction perpendicular to the plane of the frame as shown in figure. Find the magnitude and direction of the magnetic forces on the four sides of the frame.

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A proton projected in a magnetic field of 0.04 T travels along a helical path of radius 5.0 cm (of projected circle) and pitch 20 cm. Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the mass of the proton = 1.6 × 10–27 kg.

Important Questions on Magnetic Effect of Current

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A proton projected in a magnetic field of $0.04 T$ travels along a helical path of radius $5.0 cm$ (of projected circle) and pitch $20 cm$ . Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the mass of the proton $= 1.6 \times 10^{- 27} kg$ .