Two paraller long smooth conducting rails separated by a

Question

Two paraller long smooth conducting rails separated by a distance l areconnected by a movable conducting connector of mass m. Terminals of the rails are connected by the resistor R and the capacitor C as shown infig. A uniform magnetic field B perpendicular to the plane of the railis switched on. The connector is dragged by a constant force F. Find the speed of the connector as a function of time if the force F is applied at t = 0. Also find the terminal velocity of the conductor.

ROSHAN MUJEEB · Accepted Answer

Vab=Bvl,i1=BvlR,q=C(Bvl)Vab=Bvl,i1=BvlR,q=C(Bvl)
∴i2=dqdt=CBIdvdt∴i2=dqdt=CBIdvdt
Now,i=i1+i2=BvlR+CBIdvdti=i1+i2=BvlR+CBIdvdt
Magnetic forceFm=ilB=B2l2R.v+B2l2C.dvdtFm=ilB=B2l2R.v+B2l2C.dvdt
FurtherFnet=F−FmFnet=F-Fm
ormdvdt=F−B2l2Rv−B2l2Cdvdtmdvdt=F-B2l2Rv-B2l2Cdvdt
∴∫v0dvF−B2l2Rv=∫10dtm+B2l2C∴∫0vdvF-B2l2Rv=∫01dtm+B2l2C
Integrating we get,
V=FRB2l2[1−1−(B2l2mR+RB2l2C)t]V=FRB2l2[1-1-(B2l2mR+RB2l2C)t]
Terminal velocity in this case is :vT=FRB2l2

Magnetism> Two paraller long smooth conducting rails...

Navjyot Kalra , 11 Years ago

ROSHAN MUJEEB

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Ask a Doubt

Four long co-axial thin walled cylindrical conductor A, B, C and D have radii R. 2R 3R and 4R respectively. A and C carry current I and 31 respectively to plane of paper on the other hand, B and D carry and 41 respectively outward to plane of paper. Then 21

magnetism

I need solution of these questions.............................Magnetic effect of current

magnetism

A freely suspended iron rod does not point at N-S directions alwalys .why

magnetism

What is magnetic entropy change? For my knowledge, I know entropy is randomness or disorder. So here that magnetic refers to the magnetic dipole moments?

magnetism

Derive the relation between magnetic field intensity (H) and magnetization (M) for a magnetic material placed in a magnetizing field.

magnetism

Magnetism> Two paraller long smooth conducting rails...

Navjyot Kalra , 11 Years ago

ROSHAN MUJEEB

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Ask a Doubt

Other Related Questions on magnetism

Four long co-axial thin walled cylindrical conductor A, B, C and D have radii R. 2R 3R and 4R respectively. A and C carry current I and 31 respectively to plane of paper on the other hand, B and D carry and 41 respectively outward to plane of paper. Then 21

magnetism

I need solution of these questions.............................Magnetic effect of current

magnetism

A freely suspended iron rod does not point at N-S directions alwalys .why

magnetism

What is magnetic entropy change? For my knowledge, I know entropy is randomness or disorder. So here that magnetic refers to the magnetic dipole moments?

magnetism

Derive the relation between magnetic field intensity (H) and magnetization (M) for a magnetic material placed in a magnetizing field.

magnetism