Warning (2): file_get_contents(): https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eforce%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Eexerted%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Eon%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3Echarge%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Eq%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Eby%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Efield%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3EE%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Eq%3C%2Fmi%3E%3Cmover%3E%3Cmi+mathvariant%3D%22normal%22%3EE%3C%2Fmi%3E%3Cmo%3E%26rarr%3B%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi+mathvariant%3D%22italic%22%3Ealong%3C%2Fmi%3E%3Cmo+mathvariant%3D%22italic%22%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmo+mathvariant%3D%22italic%22%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo+mathvariant%3D%22italic%22%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo+mathvariant%3D%22italic%22%3E%26nbsp%3B%3C%2Fmo%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eforce%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Eexerted%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Eon%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3Echarge%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26ndash%3B%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Eq%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Eby%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Efield%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3EE%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Eq%3C%2Fmi%3E%3Cmover%3E%3Cmi+mathvariant%3D%22normal%22%3EE%3C%2Fmi%3E%3Cmo%3E%26rarr%3B%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Eopposite%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Eto%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3E%26zeta%3B%3C%2Fmi%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%26rarr%3B%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmover%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmo%3E%26rarr%3B%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%2A%3C%2Fmo%3E%3Cmover%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmo%3E%26rarr%3B%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
consider an electric dipole consisting of charges +q and –q and of length 2a placed in a uniform electric field E making an angle θ with it. It has a dipole moment of magnitude, p=q*2a
Ftotal = 0
Hence the met translating force o a dipole in a uniform electric field is zero. But the two equal and opposite forces act at different points of the dipole they form a couple which exerts a torque.
Torque = either charge*perpendicular distance between the two forces
τ=qE * 2a sin θ
As the direction of torque is perpendicular to both P and E. so we can write
Clearly, the torque on the dipole will be maximum when the dipole is held perpendicular to E. Thus
τ max = PE sin θ = PE
and minimum when angle is 00, when the dipole get aligned with E ,the torque becomes zero.
SureDen
