Magnetic vs. Electric Force Ratio – Rankers Physics
Topic: Magnetic Effects of Current
Subtopic: Force Acting on Moving Charges

Magnetic vs. Electric Force Ratio

Assertion (A): Magnetic force between two charge is generally much smaller than the electric force between them.
Reason (R): Speeds of charges are much smaller than the free-space speed of light.
 
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution:

Magnetic force \(F_m = qvB\) and electric force \(F_e = qE\). For moving charges, \(B = \frac{v}{c^2}E\). Thus, \(F_m = \frac{v^2}{c^2}F_e\). Since speeds \(v\) of charges are much smaller than the speed of light \(c\), \(F_m\) is much smaller than \(F_e\). Both (A) and (R) are true, and (R) correctly explains (A).

Leave a Reply

Your email address will not be published. Required fields are marked *