Question

(a) Find the charge on a baseball, thrown at\({\rm{35}}{\rm{.0\;m/s}}\)perpendicular to the Earth's\({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\;T}}\)field, that experiences a 1.00-N magnetic force. (b)What is unreasonable about this result?(c)Which assumption or premise is responsible?

Short answer

1. The charge on baseball is\({\rm{571C}}\).
2. Theunreasonable charge is so huge.
3. The force in question can't possibly be close to the \({\rm{1}}{\rm{.00}}\;{\rm{N}}\) force in question.

Step-by-step solution

Concept Introduction

The area of space near a magnetic body or a current-carrying body where magnetic forces caused by the body or current can be detected.

Find the charge on a baseball

(a)

The magnetic force is proportional to the particle's charge, as shown by the equation \({\rm{F}} = {\rm{q}} \times {\rm{v}} \times {\rm{B}}\).

For the charge\({\rm{q}}\), solve this equation.

\(\begin{aligned}{}{\rm{q}} &= \frac{{\rm{F}}}{{{\rm{vB}}}}\\ &= \frac{{{\rm{1}}{\rm{.00}}\;{\rm{N}}}}{{\left( {{\rm{35}}{\rm{.0\;m/s}}} \right) \times \left( {{\rm{5}}{\rm{.00}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\;T}}} \right)}}\\ &= {\rm{571}}\;{\rm{C}}\end{aligned}\)

Therefore, the charge on baseball is \({\rm{571C}}\).

Explaining the unreasonable result

(b) The charge is far too large for an object that can move freely, such as a baseball.

Explaining which assumption or premise is responsible

(c)

The Earth's magnetic field has such a weak effect that its force cannot possibly be comparable to the \({\rm{1}}{\rm{.00}}\;{\rm{N}}\) force in question.