# A charged particle of mass 0.0100 kg is subjected to a 4.0 T magnetic field which acts at a right...

## Question:

A charged particle of mass 0.0100 kg is subjected to a 4.0 T magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius 0.10 m at a speed of 5.0 m/s, what is the magnitude of the charge of the particle?

A) 0.13 C

B) 8.0 C

C) 1000.0 C

D) 0.0010 C

## Maximum Magnetic Force on a Moving Charge:

When a charged particle moves in a magnetic field, it experiences a magnetic field, and the maximum magnitude of the magnetic force (F) exerted on a moving charge is equal to the product of the charge (q) of tge particle, the speed (v) of the particle and the magnitude of the magnetic field (B) and can be expressed as:

{eq}\displaystyle{\hspace{5cm}F_{max} = qvB} {/eq}

## Answer and Explanation: 1

**We are given**

- The mass of the charged particle: {eq}m = 0.0100 \ \rm kg {/eq}

- The magnitude of the magnetic field: {eq}B = 4.0 \ \rm T {/eq}

- The radius of the circular path: {eq}r = 0.10 \ \rm m {/eq}

- The speed of the charged particle: {eq}v = 5.0 \ \rm \dfrac ms {/eq}

The magnitude of the magnetic force {eq}(F_m) {/eq} on the charged particle is given by:

{eq}\displaystyle{\hspace{5cm}F_m = qvB} {/eq}

The centrifugal force {eq}(F_c) {/eq} experienced by the particle is given by:

{eq}\displaystyle{\hspace{5cm}F_c = \dfrac{mv^2}{r}} {/eq}

From the idea of the equilibrium of the radial forces, we can write:

{eq}\displaystyle{\begin{align*} F_c &= F_m\\[0.3cm] \hspace{5cm}\dfrac{mv^2}{r} &= qvB \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)\\ \end{align*}} {/eq}

From (1), the charge of the particle is given by:

{eq}\displaystyle{\begin{align*} \hspace{5cm}q &= \dfrac{mv^2}{vB}\\[0.3cm] &= \dfrac{mv}{Br}\\[0.3cm] &= \rm \dfrac{0.0100 \ kg\times 5.0 \ \dfrac ms}{4.0 \ T\times 0.10 \ m}\times\left(\dfrac{1 \ \dfrac{C\cdot m\cdot T}{s}}{1 \ \dfrac{kg\cdot m}{s^2}}\right)\\[0.3cm] &\approx \boxed{\mathbf{0.13 \ C}}\\ \end{align*}} {/eq}

**The Correct Option**

A) **0.13 C**

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Chapter 16 / Lesson 4After completing this lab, you will be able to explain the effect of a magnetic field on moving charges, and demonstrate it using circuits and magnets. A short quiz will follow.