Explaining F=BIl and F=Bqv for Many Charges

AI Thread Summary
F = BIl and F = Bqv are equivalent expressions of the Lorentz Force Law, representing the force on a current-carrying wire and a moving charge, respectively. In the case of a wire of length l carrying a net charge q with average velocity v, the current I can be expressed as I = q/t, leading to the relationship F = BIl. The equation F = Bqv applies to a single charge moving with velocity v in a magnetic field B. Both equations involve the cross product, indicating that the force, current, and magnetic field vectors are mutually orthogonal. This demonstrates how the principles governing the force on a wire and a moving charge are fundamentally linked.
poojarao
Messages
15
Reaction score
0
Speed = distance/time and current = charge/time. Explain how F=BIl is actually the same equation as F= Bqv but considered for many charges in a group?

can someone please explain with working out please?

thanks
 
Physics news on Phys.org
Lets say that you had a wire with a length l. Let's say that traveling through that length is a net charge q, with an average velocity of v. v = distance/time, in which in this case, v = l/t. The current is I = charge/time = q/t. Therefore, F = B*q*(l/t) = B*(q/t)*l = BIl.
 
thanks a lot!
 
For clarity, these two equations (part of the Lorentz Force Law) are written as

F = l(I x B) = q(v x B)

where x indicates the cross product. meaning that the vectors F,I and B; or F,v,and B are all mutually orthogonal.
 
The I/v vectors need not be orthogonal with the B vector.
 

Thread 'Maxwell stress tensor'

This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
View full post »
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
View full post »

Similar threads

I Confused about electromotive forces
Replies
10
Views
2K
I Applying Lorentz Force correctly
Replies
1
Views
391
I Rate of work done by F on charge carrier with average velocity v
Replies
6
Views
2K
B Applying the Gauss (1835) formula for force between 2 parallel DC currents
Replies
6
Views
168
I Positive Charges: Explaining Motion Despite Net Force = 0
Replies
9
Views
2K
I Do electromagnetic fields have momentum?
Replies
15
Views
2K
I Capacitor surface charge movement current, relativistic effects
Replies
2
Views
1K
A Voltage and current waves in a transmission line
Replies
4
Views
3K
I Magnetic field as result of length contraction
Replies
20
Views
4K
I Charge movement relative to magnetic field frame dependence/invariance
Replies
5
Views
917

Hot Threads

Recent Insights

Back
Top