Moving Charges and Magnetism MCQ

Answer: b) B ⊥ v ((magnetic field B is perpendicular to v)

Explanation: According to Biot-Savart law, moving charges having velocity ’v’ produce magnetic field B which is perpendicular to the velocity. This is happening because as per the cross product rule,the magnetic field or magnetic force is always perpendicular to the velocity. Also, the magnetic field is given by:

\(d \overrightarrow{B} = {\mu_oI \over 4\pi} {(\overrightarrow{dl} \times \overrightarrow{r}) \over r^3}\)

Here, n represents the direction of B which has the same direction as the cross product of v and r i.e v x r. As a result, the magnetic field and velocity are perpendicular to each other.

Answer: a) The charge to mass ratio satisfy:(e/m)₁ + (e/m)₁ =0

Explanation: When two charged particles traverse the identical helical paths in a completely opposite sense in a uniform magnetic field like B=B₀k then they satisfy the charge to mass ratio i.e. :(e/m)₁ + (e/m)₁ =0. This is happening because the particle is thrown in some direction like a xy-plane at some angle θ with velocity v as shown in the diagram below.

Helical Motion Diagram

In this case, we need to resolve the velocity in the rectangular components which means one component is along the field i.e. v cosθ and the other one is perpendicular to the magnetic field i.e. v sinθ. Pitch is the distance covered by the particle along the magnetic field. Also, the linear distance travelled in one rotation is known as the pitch of the helix and it is given by,

p= T(v cosθ)

p= 2p (m/qB) (v cosθ)

For the given pitch p which is corresponding to the charged particle, we have

q/m = 2πv cosθ/qB = constant

This equation shows that the charged particles traverse the identical helical paths in a completely opposite sense in a uniform magnetic field B. As a result, the LHS (left-hand side) of two particles should be the same as well as of opposite sign i.e. (e/m)₁ + (e/m)₁ =0.

Answer: d) 0.3 ampere meter²(Am²)

Explanation: The magnetic dipole moment of the coil is 0.3 ampere meter²(Am²). This is calculated from the magnetic dipole moment formula such as

M = N i A

M= N i π r²

Given, radius ,r = 4 cm 

Number of turns, N= 20

Current , i = 2 ampere

Magnetic field, B = 0.5 weber/m²

Now, 

M= N i π r²

M= 20 x 2 x 3.14 x (4)²

M= 20 x 2 x 3.14 x 16 x 10-4 ampere m²

M= 0.3 ampere meter²(Am²)

Hence, the dipole moment of the coil is M= 0.3 ampere meter²(Am²).

Answer: c) By introducing a resistance of large value in series.

Explanation: The conversion of galvanometer into voltmeter is done by introducing a resistance of large value in a series. The voltmeter determines the potential difference across the points and connects in parallel between the points. The series resistance formula in galvanometer is,

Rs = G(n-1)

Where, n = V/V_g

Also, the galvanometer is a very sensitive device and gives the full-scale deflection for a very small potential difference applied across the points or terminals. So, to determine the large potential difference, an effective resistance of the device or instrument should be high. That’s why a large value of resistance is connected in series in the galvanometer. This large value of resistance is connected in series to protect the device from burning due to excessive heat produced. 

Conversion Diagram of galvanometer into voltmeter

Answer: c) An electron will continue to move with uniform velocity along the axis of the solenoid

Explanation: When an electron is projected with uniform velocity along the axis of a current carrying a long solenoid then either the electron will continue to move with uniform velocity or the electron will go undeflected along the axis of the solenoid. This is happening because at both the angles(0⁰ or 180⁰) the force is zero. Mathematically,

F = -ev B sinθ

Or F = -ev B sin180⁰

F = 0

Answer: a) Undergoes acceleration all the time

Explanation: In a cyclotron, a charged particle accelerates all the time. This is caused by the electric field which accelerates the charged particle and the magnetic field which is perpendicular to a charged particle keeps revolving in circular orbits of constant frequency.

Answer: d) mv/Be

Explanation: The radius r is mv/Be. It is given that a particle has charge e; mass=m; and moves with velocity=v in a magnetic field B. Also, the centripetal force(FC) is equal to magnetic force(FB). Mathematically,

F_C = F_B

⇒ qvB = mv²/R

⇒ R = mv/qB

⇒r = mv/Be

Answer: a) Upward.

Explanation: In this case, the direction of a magnetic field will be upward. This is happening as per Fleming's left-hand rule. According to FLeming’s rule,

Fleming’s left-hand rule Diagram

Now, 

Force is given as,

F = q v B

Here, 

F refers to force

q refers to charge

v refers to velocity

B refers to magnetic field

• The alpha particle projected towards the north which means current towards the north indicated by the middle finger.
•  particle deflected towards the East which means direction of the force towards the East indicated by thumb.
• Therefore, the direction of the magnetic field will be upward indicated by the forefinger. 

Answer: c) 1:2 

Explanation: The ratio of a magnetic field is 1:2. The value of a ratio is calculated by using a magnetic field due to the solenoid formula. Mathematically,

→ \(B = {\mu_o NI \over l}\)

As \(\mu_o\) and current (I) is constant, therefore

→ \(B \propto {N \over L}\)

→ \({B_1 \over B_2} = {N_1 \over N_2} \times {L_2 \over L_1} = {N \over 4n} \times {2l \over L} = {1 \over 2}\)

Answer: c) Represents the vector sum of the electrostatic and magnetic force acting on a moving charged particle

Explanation: Lorentz force represents the vector sum of the electrostatic and magnetic force acting on a moving charged particle. Due to the electromagnetic field, the combination of a magnetic and electric force on a point is known as a lorentz force. A particle which has a charge q and moves with the velocity v in the presence of an electric field and a magnetic field experiences the force which is called a lorentz force. Mathematically,

F = q E + qv x B

Here, 

q ⇒ refers the charge

V⇒ refers the velocity

E⇒ refers the electric field

B⇒ refers the Magnetic field 

Answer: d) Both b and c.

Explanation: Magnetic fields can be produced by changing electric fields as well as moving charges. In a charge, the number of electrons and protons present in a nucleus. When the charge is in motion then the electric field changes. As a result, a magnetic field produces.

Answer: c) Zero.

Explanation: The value of the magnetic field at any point on the axis of a current element is zero. This is happening because the angle made between the axis of a linear axis and the distance is zero. So, the magnetic field at this point is zero. Mathematically, at an angle θ=00, the magnetic field is given as:

 \(dB = {\mu_o \over 4 \pi} {Idlsi0^0 \over r^2}\)

dB = 0