Force on a moving charge in magnetic and electric fields — practice questions

Question 1 · difficulty L1 · recall

The magnetic part of the Lorentz force on charge q moving with velocity v is

• A. q(v × B)
• B. q(v · B)
• C. qB/v
• D. qE × B

Question 2 · difficulty L1 · understanding

A charged particle moves exactly parallel to a uniform magnetic field. The magnetic force on it is

• A. qvB
• B. zero
• C. qB/v
• D. qvB/2

Question 3 · difficulty L2 · understanding

Which statement about a magnetic force on a moving charged particle is correct?

• A. It always increases the particle's speed
• B. It always decreases kinetic energy
• C. It changes the direction of velocity but does no work in a purely magnetic field
• D. It acts parallel to the velocity

Question 4 · difficulty L2 · application

A positive charge moves east in a magnetic field directed north. The magnetic force points

• A. downward
• B. eastward
• C. westward
• D. upward

Question 5 · difficulty L2 · understanding

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path. Reason (R) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

• A. (A) is true but (R) is false
• B. Both (A) and (R) are true and (R) is the correct explanation of (A)
• C. Both $(\mathbf{A})$ and $(\mathbf{R})$ are true but $(\mathbf{R})$ is NOT the correct explanation of (A)
• D. (A) is false but (R) is true

Question 6 · difficulty L2 · understanding

A proton and a deutron $$(q=+\mathrm{e}, m=2.0 \mathrm{u})$$ having same kinetic energies enter a region of uniform magnetic field $$\vec{B}$$, moving perpendicular to $$\vec{B}$$. The ratio of the radius $$r_d$$ of deutron path to the radius $$r_p$$ of the proton path is:

• A. $$1: 2$$
• B. $$1: 1$$
• C. $$\sqrt{2}: 1$$
• D. $$1: \sqrt{2}$$

Question 7 · difficulty L2 · understanding

The electrostatic force $$\left(\vec{F_1}\right)$$ and magnetic force $$\left(\vec{F}_2\right)$$ acting on a charge $$q$$ moving with velocity $$v$$ can be written :

• A. $$\vec{F}_1=q \vec{B}, \vec{F}_2=q(\vec{B} \times \vec{v})$$
• B. $$\vec{F}_1=q \vec{V} \cdot \vec{E}, \vec{F}_2=q(\vec{B} \cdot \vec{V})$$
• C. $$\vec{F}_1=q \vec{E}, \vec{F}_2=q(\vec{V} \times \vec{B})$$
• D. $$\vec{F}_1=q \vec{E}, \vec{F}_2=q(\vec{B} \times \vec{V})$$

Question 8 · difficulty L2 · understanding

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

• A. the electron will experience a force at $$45^{\circ}$$ to the axis and execute a helical path.
• B. the electron will be accelerated along the axis.
• C. the electron path will be circular about the axis.
• D. the electron will continue to move with uniform velocity along the axis of the solenoid.

Question 9 · difficulty L2 · understanding

Two particles $$X$$ and $$Y$$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $$R_1$$ and $$R_2$$ respectively. The mass ratio of $$X$$ and $$Y$$ is :

• A. $$\left(\frac{R_1}{R_2}\right)$$
• B. $$\left(\frac{R_2}{R_1}\right)$$
• C. $$\left(\frac{R_2}{R_1}\right)^2$$
• D. $$\left(\frac{R_1}{R_2}\right)^2$$

Question 10 · difficulty L2 · understanding

Given below are two statements : Statement I : The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle. Statement II : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both Statement I and Statement II are correct.
• B. Both Statement I and Statement II are incorrect.
• C. Statement I is correct but Statement II is incorrect.
• D. Statement I is incorrect but Statement II is correct.